histogram problem solving tool

Histogram Calculator

Welcome to our cutting-edge Histogram Calculator, a remarkable tool engineered to facilitate the visualization and understanding of your numerical data distribution. This tool is designed to cater to the needs of data enthusiasts across the globe.

Unveiling the Concept of a Histogram

A histogram is a graphical representation that organizes a group of data points into specified ranges or 'bins'. These bins are showcased on the x-axis, while the y-axis displays the frequency of data points within each bin. Essentially, a histogram provides a visual narrative of numerical data, representing the count of data points that fall within a specified range of values (the 'bins').

Decoding Histograms - A Key to Data Visualization

Histograms serve as a cornerstone in the fields of statistical analysis and data visualization. They render an overview of data distribution, assisting in the identification of patterns such as central tendency, dispersion, skewness, and the presence of outliers.

In a histogram, the area of each bar signifies the count of values within a particular bin. The contour of the histogram can offer valuable insights into the underlying distribution pattern (like normal, exponential, etc.) and its parameters.

Delving into the Working of our Histogram Calculator

Our Histogram Calculator offers a smooth and user-friendly approach to generate histograms. It presents two modes for calculating histograms: Automatic and Manual.

Automatic Mode

In Automatic mode, the calculator determines the optimal number of bins by implementing the Freedman-Diaconis rule . This rule utilizes the interquartile range (IQR) and the cube root of the total number of data points in its calculation. The IQR is the range between the first quartile (25th percentile) and the third quartile (75th percentile) of the data.

The Freedman-Diaconis rule calculates the bin width (h) as follows:

h = 2 * \text{IQR} * N^{\frac{-1}{3}}

Here, N denotes the number of data points.

Subsequently, the number of bins (k) is computed by dividing the total range of the data (R) by the bin width:

k = \dfrac{R}{h}

The Freedman-Diaconis rule is particularly effective for datasets characterized by skewed or bimodal distributions, large datasets with a myriad of unique values, and datasets that comprise both integer and floating-point numbers.

Manual Mode

In the Manual mode, you have full control over the histogram parameters. You can specify the:

• Number of bins
• Highest x value
• Lowest x value

The manual mode gives you the flexibility to customize the histogram to your specific needs. However, it requires an understanding of the data and how histograms work.

Bin Labeling

Our Histogram Calculator also offers three options for labeling the bins:

• Middle - Each bin is labeled by its middle value.
• Edge - Each bin is labeled by its edge value (lower, upper).
• Custom - You have the option to specify your own labels for the bins. (Note! Number of custom labels should match number of bins.)

How to Use Our Histogram Calculator?

Using our Histogram Calculator is straightforward:

• Enter your data into the input field. Data points should be comma or space separated.
• Choose the mode - 'Automatic' or 'Manual'. If you choose 'Manual', fill in the additional parameters.
• Choose how you would like the bins to be labeled.
• Our calculator will automatically generate the histogram for you.

By providing a comprehensive understanding of your data's distribution, histograms are an invaluable tool in many fields, including statistics, data analysis, machine learning, and more. Our Histogram Calculator is designed to assist you in these tasks, giving you a powerful tool to understand and analyze your data effectively.

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The Histogram tool creates individual and cumulative frequencies for a range of cells and specified number of bins.  A histogram uses bars (or rectangles) of different heights to display the frequency, or number of records, in the population. 

The example below contains sales of Mark's Milk Chocolate Bars for the month of January for a small candy shop.

To create a histogram:

• On the XLMiner Analysis ToolPak pane, click Histogram
• Enter B1:B32 for "Input Range". 
• Enter C1:C6 for "Bin Range".  This range includes the upper bound of five (n) data "bins" or categories.  Six bins (or n + 1) will appear in the histogram:  0-5, 6-10, 11-15, 16-20, 21-25, and More.  Any records with values greater than 25 will be placed in the More bin. 
• Keep "Labels" selected since the first row contains labels describing the contents of each column. 
• Enter E1 for "Output Range".
• Select "Pareto" to add a column listing the frequency values from greatest to least and the cumulative percentages of observations assigned to each bin. 
• Select "Cumulative Percentage" to add a column that computes the cumulative number of observations and related percentages for each bin.   
• Select "Chart Output" to display the Histogram. Click OK. 

The results are below. 

In this example, 2 observations were assigned to the 0-5 bin, 16 assigned to the 6-10 bin, 6 assigned to the 11-15 bin, 5 observations to the 16-20 bin and 2 observations to the 21-25 bin. 

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Histogram As A Component Of Seven Basic Quality Tool

• Project Management

Histogram As A Component Of Seven Basic Quality Tools

In the Project Management Professional (PMP) exam, histograms are valuable quality planning and control tools. A histogram visualizes two variables that are particularly helpful when sharing information about issues, defects, or quality-related matters with stakeholders. For example, a histogram can present the reasons for defects on one axis and the corresponding number of defects caused by each reason on the other axis. The frequencies of these reasons are displayed as adjacent rectangles. This graphical representation enables stakeholders to identify areas with more defects that need improvement.

Furthermore, analyzing the height of the bars or adjacent rectangles in the histogram allows for a deeper understanding. It helps in identifying the appropriate corrective or preventive actions to address the identified issues.

In the context of the PMP, the Histogram is defined as:

A histogram is a type of bar chart that is used to represent the central tendency (average or mean), dispersion (variability), and pattern of statistical distribution in a visual and easy-to-understand manner.

Let’s look at a case study for the Development of Histogram

To make a histogram, we need a check sheet as an input. To get more details about the check sheet, please refer to the Blog  Check Sheet as a Component of Seven Basic Quality Tool ;

I am using the same example used in the check sheet as a reference. Let’s reiterate the same example used in the check sheet –

An IT test team member is evaluating work products from specifications to detect problems. The team may choose to categorize data about quality problems in the following categories as suggested by Roger S. Pressman:

• Incomplete or erroneous specification (IES)
• Misinterpretation of customer communication (MCC)
• Intentional deviation from specifications (IDS)
• Violations of programming standards. (VPS)
• Error in data representations (EDR)
• Inconsistent component interface (ICI)
• Error in design logic (EDL)
• Incomplete or erroneous testing (IET)
• Inaccurate or inconsistent documentation (IID)
• Error in programming language translation of design (PLT)
• Ambiguous or inconsistent human/computer interface (HCI)
• Miscellaneous (MIS)

While examining the work product, test team member assesses the defects and enter frequencies in their respective category of causes like:

Check Sheet suggested by roger s. pressman in software engineering a practitioner’s approach

As a further explanation, the first two columns are used to develop a Histogram, as shown below:

As mentioned below, using Excel, we can develop Histogram,

Usages of Histogram:

1. In Quality Planning: In this histogram, frequencies of issues in “IES”, “MCC”, and “EDR” are higher; you may choose to focus on enhancing the “Collecting Requirement” and “Defining Scope” processes as part of improvement efforts. The Histogram helps identify areas where improvements will have the most significant impact on quality. So, the histogram is a valuable tool for planning quality and taking preventive measures to improve processes.

2. In Quality Control: Histograms are a powerful tool in quality control as they help identify causes of poor performance and enable improvements in processes and work products. By analyzing the data represented in a histogram, corrective actions can be taken to address the identified issues and enhance overall quality.

3. In Agile Project Management: Histograms are also a valuable tool in Agile for visualizing data and facilitating data-driven decision-making . In an iteration retrospective, you can use a histogram to analyze the frequency of different types of defects, issues, or impediments encountered. For example, you can create a histogram showing the number of defects reported per iteration to identify recurring patterns and prioritize actions to improve quality. Similarly, during an iteration review, a histogram can be used to present data on completed user stories. For instance, the team can create a histogram to display the distribution of story points completed, helping stakeholders understand the progress in the iteration.

Difference between Pareto Chart and Histogram: The main difference between a Pareto chart and a histogram lies in the purpose they serve:

A histogram is a bar chart commonly used in Total Quality Management (TQM). It shows the frequency of a cause of a problem occurring where the height of the bar is an indicator of the most affecting reason. For a visual presentation and further understanding of histograms, you can watch this video:

Frequently Asked Questions:

Q: what is a histogram in project management.

Answer:  It is a tool to visually represent the causes of problems that are most affecting the given situation. It helps to understand the area which needs your focus to take corrective, preventive actions.

Q: What is the importance of histograms?

Answer:  A histogram is a popular tool for analyzing large data.  After analysis, it forms a bar chart to show influential factors that causes problems.

Q: What are the features of a histogram?

Answer:  The histogram breaks up the range of possible values in groups measured in an interval scale. It shows data distribution in a convenient form to help discover appropriate corrective and preventive actions.

Q: What is the difference between the histogram and Pareto chart?

Answer:  A histogram is a kind of bar chart where the bar’s height shows the event’s frequency. A Pareto chart is a special histogram where data are displayed using the 80/20 rule. Here most significant 20% of causes are visually presented in descending order of frequency.

I trust that this blog has effectively addressed all your inquiries regarding histograms and their significance in quality planning and control.

If you have aspirations to pursue the PMP certification,  enroll with us   for comprehensive support in your PMP certification journey. We offer expert guidance in exam preparation, assistance with the application process, and help in scheduling the exam. With our assistance, you can confidently navigate the certification process and increase your chances of success.

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PMP Exam Practice Questions

As you prepare for the PMP Certification Exam, we’re thrilled to present our latest addition: a set of carefully curated practice questions. Designed to closely reflect the actual PMP exam’s complexity and style, these questions cover key domains including People, Process, and Business Environment, as outlined in the PMP Exam Content Outline (ECO) . Each question is complemented by video explanations, offering deeper insights and enhancing your learning experience. Check Out PMP Questions

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Histogram: The way of data analysis and QC tool

As been a Quality Engineer or Industrial Engineer we must know the 7 QC tools. And one of the important QC tool is Histogram.

In this post you will learn more details about this tool. How and the way of data analysis using the important QC tool.

Table of Contents

What is Histogram?

Histogram is the visual tool for presenting the variable data. And also it organize the data to describe the process performance .

Additionally it shows the amount and pattern of the variation from the process. The date you collected will be arrange in manner, it will show you the variation and spread of data.

Therefore it is the most powerful tool in 7 QC tools .

Why do we get variation?

Variation is essentially a law of nature. Therefore we can’t eliminate the variation.

Output quality characteristics depend upon the input parameters.

It is impossible to keep input parameters constant. There will be always variation in the input parameters. Since there is variation in the input parameters, there is also variation in the output characteristics

Learn more about why do we get variation?

Definition of Histogram

The pictorial nature of the histogram enables us to see patterns that are difficult to see in a table of numbers.

Key Concept of Histogram

• Data always have variation
• Variation have pattern
• Patterns can be seen easily when summarized pictorially

Example with data

Data Table – Weight of Bars in kg.

Study of Histogram

So, now you draw the graph base on the data you have. But if you dont know how to study it then no use. Therefore here are some points which you should look into it and interpret the data. Refer below points:

•   Location of mean of the process
•   Spread of the process
•   Shape of the process

Constructing Histogram

Basic Elements for Construction of Histogram

For constructing it we need to know the following:

• Lowest value of the data set
• Highest value of the data set
• Approximate number of cells graph have
• Lower cell boundary of first cell

Related Posts

Control Charts & Types of control chart

Cause and Effect Analysis

Pareto Analysis – 7 QC Tool

Scatter Diagram in 7 QC tools | Draw a scatter diagram

Flow Chart Guide – 7 QC tool

Ishikawa Tools

The ishikawa tools (also known as seven basic tools) are made up of the cause-effect diagram, check sheet, control chart, histogram, pareto chart, scatter diagram, and stratification..

The Ishikawa Tools – sometimes called the seven basic tools of Six Sigma – are simple but effective tools to address complex quality control challenges. They offer a great place to start for those new to Six Sigma methodology .

Those with a basic understanding of statistics can use the Ishikawa tools. They are named after Japanese engineer Kaoru Ishikawa, an important figure in the development of kaizen (continuing process improvement). The tools are frequently used in quality circles, a term for groups of workers who do similar jobs or work together on an operational process. They meet regularly to identify, analyze and find solutions to work-related problems.

The Ishikawa Tools (Seven Basic Tools)

The following tools make up the Ishikawa Tools. Some may also refer to them as the seven basic tools of Six Sigma.

Cause and Effect Diagram

The cause and effect diagram (also known as a fishbone diagram) provides an easy-to-understand visual that starts with a problem, then lists the causes, sub causes and sub causes of the sub causes until reaching the root cause of the issue. Teams use the fishbone diagram to better solve reoccurring problems.

Check Sheet

A check sheet offers a structured table that allows teams to list problems on the left-hand side, and then provide information on the right of each on the topics such as the frequency and severity of the problem.

Control Chart

A control chart tracks process change over time. Teams use current process data and determine if process variation is consistent (under control) or unpredictable (out of control). If out of control, then teams must use other tools to determine the root cause of the problem.

The histogram is a graph that shows frequency distributions for a specific data set. For example, traffic engineers might use a histogram to record the number of people who pass through an intersection at different times of day. A retail outlet might determine staffing levels for every hour of the way by creating a histogram that tracks the number of customers who come through the door at different times on every day of the week.

Pareto Chart

Named after Italian economist Vilfredo Pareto, the Pareto Chart works on the theory that 80% of process problems occur because of mistakes in 20 percent of the factors involved in the process. The Pareto Chart helps teams identify the most significant factors in a process, allowing them to focus on improving the most important aspects of a process.

Scatter Diagram

A scatter diagram involves placing plot points on an X and Y axis for two different sets of data, providing a visual that quickly can show the relation between two sets of data. A simple example is a chart of hurricanes in one year (one data set) and the months of the year they occurred (a second data set). This quickly establishes what months of the year that require the most hurricane preparation.

Stratification

The process of stratification involves taking a data set and breaking it down into categories that provide more insight. For instance, a manager might have data showing the dates that their employees show up late for work. But by further breaking that data down into days of the week, they can quickly see what days where lateness most frequently occurs (Monday, most likely).

Histogram : a graphical display of data using bars of different heights.

It is similar to a Bar Chart , but a histogram groups numbers into ranges .

The height of each bar shows how many fall into each range.

And you decide what ranges to use!

Example: Height of Orange Trees

You measure the height of every tree in the orchard in centimeters (cm)

The heights vary from 100 cm to 340 cm

You decide to put the results into groups of 50 cm:

• The 100 to just below 150 cm range,
• The 150 to just below 200 cm range,

So a tree that is 260 cm tall is added to the "250-300" range.

And here is the result:

You can see (for example) that there are 30 trees from 150 cm to just below 200 cm tall

(PS: you can create graphs like that using Make your own Histogram )

Notice that the horizontal axis is continuous like a number line :

Example: How much is that puppy growing?

Each month you measure how much weight your pup has gained and get these results:

0.5, 0.5, 0.3, −0.2, 1.6, 0, 0.1, 0.1, 0.6, 0.4

They vary from −0.2 (the pup lost weight that month) to 1.6

Put in order from lowest to highest weight gain:

−0.2, 0, 0.1, 0.1, 0.3, 0.4, 0.5, 0.5, 0.6, 1.6

You decide to put the results into groups of 0.5:

• The −0.5 to just below 0 range,
• The 0 to just below 0.5 range,

(There are no values from 1 to just below 1.5, but we still show the space.)

The range of each bar is also called the Class Interval

In the example above each class interval is 0.5

Histograms are a great way to show results of continuous data , such as:

• how much time

But when the data is in categories (such as Country or Favorite Movie), we should use a Bar Chart .

Frequency Histogram

A Frequency Histogram is a special graph that uses vertical columns to show frequencies (how many times each score occurs):

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Histogram – 7 QC Tools for Graphical Analysis

By OpEx Learning Team , Last Updated January 10, 2014

Histogram – 7 QC Tools for Graphical Analysis is one of the most simplest and helpful tools used in Lean and Six Sigma. It is one of the 7 QC Tools (Quality Control Tools). It is a graphical analysis chart that helps us to see, not necessarily infer, conclusions from a data set. A Histogram allows us to see the shape of your data set. In this 3:01 minute HD video, you will learn the following:

• What is a Histogram
• When to use a Histogram
• How to create a Histogram

This video on the Histogram is part of our video training series on the 7 Quality Tools as used in Lean and Six Sigma. Enjoy the video below.

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• What is a Histogram? What is the Purpose of a Histogram? – 7 QC Tools

by admin | Nov 20, 2020 | General , Manufacturing , Quality | 0 comments

Histogram – 7 QC Tools

Histogram  is a bar graph which shows the distribution of data. It shows the snap shot of the data taken from a process .

The Purpose of Histogram is to

• Summarize large data sets graphically
• Compare measurements to specifications
• Assist in decision making during problem solving

The Data spread in the process is the result of the variation that exists in the process.

Histogram helps us to understand that with the prevailing variation the process is capable to produce within the specifications. This is done by just superimposing the Specification Limits with the Histogram drawn

The above example indicates that the process is well capable as the variability of the process data is well within the specification

There is always possibilities of a capable process to produce defects if the setting parameters is not in line with the specification Mean. Histogram also help to understand the setting of a process is line with the specification.

The above example indicates that the variability in the process is very less compared to the specification limits indicating that the process is a capable process. However a pile of data fall outside the specification limits producing defects. This is due to the poor setting parameters.

In statistical terms histogram Helps us to

• know the central value of the data (setting)
• know the spread (variation) in the data
• assess the ability of the process to meet the specifications
• estimate the extent of non-conformance in the process output
• understand whether the non-conformance is due to setting or due to variation

Histogram is a powerful tool helps to understand the process in just a glimpse. It helps in decision making during  Problem solving .

Few books recommended to read on Problem solving and Histogram are given below

• Management for Quality Improvement: The 7 New QC Tools
• QUALITY CONTROL TOOLS: 7 QC TOOLS
• Seven Basic Quality Tools
• 7 QC Tools: Problem Solving Tools
• 7 QC tools for process improvement

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Guide: Histogram

Author: Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

A histogram is similar to a bar chart, but it is a precise tool for showing the frequency of data across intervals. Picture a set of data points, such as the times it takes to complete a manufacturing process. These points are segmented into “bins,” each an equal width, and tallied to reflect how often values land within these slices of the data spectrum. This graphical representation is important in Lean Six Sigma, where understanding the spread and shape of data distribution is key. Whether data is tightly clustered or broadly spread, histograms transform numbers into visual stories, revealing process variations and guiding continuous improvement.

What is a Histogram?

If you look at a Histogram, you might think it looks like a bar chart, it is in fact a type of bar chart. The Histogram represents the frequency of numerical data distribution. To create a histogram the range of data is divided into intervals, and then the frequency of the data points within each interval is tallied. These intervals are known as “bin”, and they are usually equally sized in terms of width with a high dependence on frequency. 

Key Components of Histograms

• Bins: These are the defined intervals that cover a range of data; for example above, you have 1-2 being a bin, then 2-3 as another bin. So where the data point value is between 1 and 2, it would fall within the first bin frequency.
• Frequency:  This is the count of data points within each bin. The frequency can either be absolute or relative (a percentage of the total number of data points).

Importance in Lean Six Sigma

In Lean Six Sigma, histograms are a useful data analysis tool that is used to understand data in terms of frequency and distribution. Histograms are used in Lean Six Sigma projects for:

• Process understanding: Histograms are able to provide a visualization of data to show how much variation there is in a process. This can be done by examining the spread and shape of the distribution. By using a Histogram you can understand if there is too much variation as an output of your process and see to what degree and in which direction it needs to be shifted or reduced.

• Data Analysis:  Reviewing raw data it can be difficult to come to any conclusions as raw data can be large and difficult to read. By using a histogram, it can reveal patterns that may not be evident. A histogram could be normally distributed, skewed positive or negativley, or could have a bimodal distribution, which might suggest that two different processes or groups have been merged.

Normal Distribution

Right Skewed Distribution

Left Skewed Distribution

Biomodal Histogram

• Continuous Improvement:  By identifying and understanding the distribution of data, histograms can show areas of a process that need to be improved. For example, if the histogram shows that a significant number of outputs are outside customer specifications, the process may need to be centred or variation reduced.

Creating a Histogram

Creating histograms these days is relatively simple with software such as Excel. We also have a free histogram download template that you can paste data into for results.

We have also developed a web-based tool that will allow you to upload or paste a data file, which will create a Histogram and analyze the data in it for you. Feel free to try out the Histogram Analyzer tool .

Aside from those two options, follow our guide below on creating your histogram:

Step 1: Data Collection

Before you can visualize your data, you need to collect it if you have not already.

You will do this by identifying the data source , it could be process measurements, time studies, or customer satisfaction surveys. The data you will need for this is numerical can can be on a continuous scale so does not need to be whole numbers.

Once you know what data to collect, you need to collect it and ensure it is structured in the right format. 

After data collection, it is important to clean the data and by this, we mean to ensure no outliers or errors in the data are removed as they could skew the results.

Step 2: Data Arrangement

Following the collection and cleaning of data the next step would be to  sort  the data, which means you need to arrange the data from smallest to largest values.

Next in Excel, select all of your data, click  Insert  > Recommended Charts > All Charts > Histogram > Ok

You will then have your Histogram.

Step 3: Interpreting the Histogram

When reviewing a histogram, you’re analyzing the data it represents. Here’s how to analyze a histogram and what to look for:

• Balanced Process : A symmetric histogram, where data is evenly spread around a central value, suggests that the process is consistent and predictable.
• Example : If you’re measuring the weight of packaged products and the histogram is symmetric around the target weight, this indicates that your packaging process is accurate on average.
• Process Bias : Skewness in a histogram indicates that the data is not evenly distributed around the central value.
• Right-Skewed : More data is concentrated on the left side, suggesting frequent low-value occurrences and some high-value outliers. In terms of process, this could mean that while most operations are fast, a few take much longer.
• Left-Skewed : More data is concentrated on the right, indicating that high values are more common and low values are outliers. For product quality, this might imply that most products are over the desired specification limit, with only a few meeting the target.
• Isolated Bars : Outliers appear as bars that are separate from the main body of the histogram. They can indicate special causes that may not be part of the normal process variation.
• Investigation : Outliers should be investigated to determine their cause. They might result from measurement errors, unusual events, or changes in the process.

In Lean Six Sigma, histograms are more than just graphs; they visualize data to understand how a process is performing. By arranging numerical data into visually compelling stories, histograms help in determining the predictable from the abnormal.

They highlight whether a process is symmetrical or skewed, whether it’s meeting targets or veering off course. With tools like Excel and our Histogram Analyzer , crafting these insightful charts is within anyone’s grasp. Remember, each bar holds a clue, and outliers require deeper exploration.

• Scott, D.W., 1979. On optimal and data-based histograms.   Biometrika ,  66 (3), pp.605-610.
• Guha, S., Koudas, N. and Shim, K., 2001, July. Data-streams and histograms. In  Proceedings of the thirty-third annual ACM symposium on Theory of computing  (pp. 471-475).

Q: What is a histogram?

A: A histogram is a graphical representation of the distribution of numerical data. It consists of a series of bars, where each bar represents a range of values called a bin. The height of each bar represents the frequency or count of data points falling within that bin.

Q: What is the purpose of a histogram?

A: The purpose of a histogram is to visualize and understand the distribution of data. It allows you to identify patterns, trends, and outliers in the data. Histograms are particularly useful for analyzing continuous or interval data and are commonly used in fields such as statistics, data analysis, and research.

Q: How do I determine the number of bins for a histogram?

A: The number of bins in a histogram can be determined using various methods. A common rule of thumb is to use the square root of the total number of data points. However, you can also consider the nature of your data and the level of detail you want to display. Experimenting with different bin numbers and assessing the resulting visualization can help you find the most suitable number of bins.

Q: What is bin width?

A: Bin width refers to the size or interval of each bin in a histogram. It is calculated by dividing the range of the data by the number of bins. A smaller bin width provides more detailed information but may result in a cluttered histogram, while a larger bin width provides a more general overview but may obscure important details.

Q: Can I customize the appearance of a histogram?

A: Yes, you can customize the appearance of a histogram to make it more visually appealing and informative. You can choose different colors for the bars, add labels and titles, adjust the axis scales, and include additional graphical elements such as shading or overlays. Customizing the histogram can enhance its clarity and help convey the intended message effectively.

Q: How do I interpret a histogram?

A: To interpret a histogram, analyze the shape, peaks, and gaps in the distribution. Look for patterns, such as symmetry or skewness, that can provide insights into the underlying data. Compare the histogram to expected or theoretical distributions to draw meaningful conclusions. Consider outliers or unusual data points and their implications. The interpretation of a histogram is subjective and depends on the context of the data and the research question being addressed.

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7 Basic Tools of Quality for Process Improvement

Japan is known worldwide for its quality products and services. One of the many reasons for this is its excellent quality management. How did it become so? Japan has Dr. Kaoru Ishikawa to thank for that.

Postwar Japan underwent a major quality revolution. Companies were focused on training their employees in statistical quality control. But soon they realized that the complexity of the subject itself could intimidate most of the workers; so they wanted more basic tools.

Dr. Kaoru Ishikawa, a member of the Japanese Union of Scientists and Engineers (JUSE), took it to his hands to make quality control easier for everyone – even those with little knowledge of statistics – to understand. He introduced the 7 basic tools of quality. They were soon adopted by most companies and became the foundation of Japan’s astonishing industrial resurgence after World War 2.

This post will describe the 7 basic quality tools, how to use them and give you access to templates that you can use right away.

Quality Tools: What Are They?

How can teams and organizations use the 7 basic quality tools, cause and effect diagram, scatter diagram, check sheets.

• Control chart
• Pareto chart

The 7 basic tools of quality, sometimes also referred to as 7 QC tools – represent a fixed set of graphical tools used for troubleshooting issues that are related to quality.

They are called basic quality tools because they can be easily learned by anyone even without any formal training in statistics. Dr. Kaoru Ishikawa played the leading role in the development and advocacy of using the 7 quality tools in organizations for problem-solving and process improvement.  

The 7 basic quality tools include;

• Cause-and-effect diagram
• Scatter diagram
• Check sheet

The 7 quality tools were first emphasized by Kaoru Ishikawa a professor of engineering at the University of Tokyo, who is also known as the father of “Quality Circles” for the role he played in launching Japan’s quality movement in the 1960s. During this time, companies were focused on training their employees in statistical quality control realized that the complexity of the subject could intimidate most of the workers; hence they opted for simpler methods that are easy to learn and use. 7 basic tools of quality were thus incorporated company-wide.

Quality tools are used to collect data, analyze data, identify root causes, and measure results in problem-solving and process improvement. The use of these tools helps people involved easily generate new ideas, solve problems, and do proper planning.

• Structured approach: They provide a systematic approach to problem-solving and process improvement, ensuring that efforts are well-organized and focused.
• Data-driven decision making: The tools enable data collection, analysis, and visualization, empowering teams to make informed decisions based on evidence.
• Improved communication and collaboration: Visual representations and structured tools facilitate effective communication and collaboration among team members, leading to shared understanding and alignment.
• Problem identification and prioritization: The tools help identify and prioritize problems or improvement opportunities, enabling teams to allocate resources efficiently and address critical issues first.
• Continuous improvement: By using these tools, teams can establish a culture of continuous improvement, as they provide a framework for ongoing monitoring, analysis, and refinement of processes.

7 Basic Quality Tools Explained with Templates

The 7 quality tools can be applied across any industry.  They help teams and individuals analyze and interpret the data they gather and derive maximum information from it.

Flowcharts are perhaps the most popular out of the 7 quality tools. This tool is used to visualize the sequence of steps in a process, event, workflow, system, etc. In addition to showing the process as a whole, a flowchart also highlights the relationship between steps and the process boundaries (start and end).

Flowcharts use a standard set of symbols, and it’s important to standardize the use of these symbols so anyone can understand and use them easily. Here’s a roundup of all the key flowchart symbols .

• To build a common understanding of a process.
• To analyze processes and discover areas of issues, inefficiencies, blockers, etc.
• To standardize processes by leading everyone to follow the same steps.

Real-world examples of usage

• Documenting and analyzing the steps involved in a customer order fulfillment process.
• Mapping out the workflow of a software development lifecycle.
• Visualizing the process flow of patient admissions in a hospital.

Enhances process understanding, highlights bottlenecks or inefficiencies, and supports process optimization and standardization efforts.

How to use a flowchart

• Gather a team of employees involved in carrying out the process for analyzing it.
• List down the steps involved in the process from its start to end.
• If you are using an online tool like Creately , you can first write down the process steps and rearrange them later on the canvas as you identify the flow.
• Identify the sequence of steps; when representing the flow with your flowchart, show it from left to write or from top to bottom.
• Connect the shapes with arrows to indicate the flow.

Who can use it?

• Process improvement teams mapping and documenting existing processes for analysis.
• Business analysts or consultants analyzing workflow and process optimization opportunities.
• Software developers or system designers documenting the flow of information or interactions in a system.

To learn more about flowcharts, refer to our Ultimate Flowchart Tutorial .

A histogram is a type of bar chart that visualizes the distribution of numerical data. It groups numbers into ranges and the height of the bar indicates how many fall into each range.

It’s a powerful quality planning and control tool that helps you understand preventive and corrective actions.

• To easily interpret a large amount of data and identify patterns.
• To make predictions of process performance.
• To identify the different causes of a quality problem.
• Analyzing the distribution of call wait times in a call center.
• Assessing the distribution of product weights in a manufacturing process.
• Examining the variation in delivery times for an e-commerce business.

Provides insights into process performance and variation, enabling teams to target areas for improvement and make data-driven decisions.

How to make a histogram

• Collect data for analysis. Record occurrences of specific ranges using a tally chart.
• Analyze the data at hand and split the data into intervals or bins.
• Count how many values fall into each bin.
• On the graph, indicate the frequency of occurrences for each bin with the area (height) of the bar.
• Process engineers or data analysts examining process performance metrics.
• Financial analysts analyzing expenditure patterns or budget variances.
• Supply chain managers assessing supplier performance or delivery times.

Here’s a useful article to learn more about using a histogram for quality improvement in more detail.

This tool is devised by Kaoru Ishikawa himself and is also known as the fishbone diagram (for it’s shaped like the skeleton of a fish) and Ishikawa diagram.

They are used for identifying the various factors (causes) leading to an issue (effect). It ultimately helps discover the root cause of the problem allowing you to find the correct solution effectively.

• Problem-solving; finding root causes of a problem.
• Uncovering the relationships between different causes leading to a problem.
• During group brainstorming sessions to gather different perspectives on the matter.
• Investigating the potential causes of low employee morale or high turnover rates.
• Analyzing the factors contributing to product defects in a manufacturing process.
• Identifying the root causes of customer complaints in a service industry.

Enhances problem-solving by systematically identifying and organizing possible causes, allowing teams to address root causes rather than symptoms.

How to use the cause and effect diagram

• Identify the problem area that needs to be analyzed and write it down at the head of the diagram.
• Identify the main causes of the problem. These are the labels for the main branches of the fishbone diagram. These main categories can include methods, material, machinery, people, policies, procedures, etc.
• Identify plausible sub-causes of the main causes and attach them as sub-branches to the main branches.
• Referring to the diagram you have created, do a deeper investigation of the major and minor causes.
• Once you have identified the root cause, create an action plan outlining your strategy to overcome the problem.
• Cross-functional improvement teams working on complex problems or process improvement projects.
• Quality engineers investigating the root causes of quality issues.
• Product designers or engineers seeking to understand the factors affecting product performance.

The scatter diagram (scatter charts, scatter plots, scattergrams, scatter graphs) is a chart that helps you identify how two variables are related.

The scatter diagram shows the values of the two variables plotted along the two axes of the graph. The pattern of the resulting points will reveal the correlation.  

• To validate the relationship between causes and effects.
• To understand the causes of poor performance.
• To understand the influence of the independent variable over the dependent variable.
• Exploring the relationship between advertising expenditure and sales revenue.
• Analyzing the correlation between employee training hours and performance metrics.
• Investigating the connection between temperature and product quality in a production line.

Helps identify correlations or patterns between variables, facilitating the understanding of cause-and-effect relationships and aiding in decision-making.

How to make a scatter diagram

• Start with collecting data needed for validation. Understand the cause and effect relationship between the two variables.
• Identify dependent and independent variables. The dependent variable plotted along the vertical axis is called the measures parameter. The independent variable plotted along the horizontal axis is called the control parameter.
• Draw the graph based on the collected data. Add horizontal axis and vertical axis name and draw the trend line.
• Based on the trend line, analyze the diagram to understand the correlation which can be categorized as Strong, Moderate and No Relation.  
• Data analysts exploring relationships between variables in research or analytics projects.
• Manufacturing engineers investigating the correlation between process parameters and product quality.
• Sales or marketing teams analyzing the relationship between marketing efforts and sales performance.

Check sheets provide a systematic way to collect, record and present quantitative and qualitative data about quality problems. A check sheet used to collect quantitative data is known as a tally sheet.

It is one of the most popular QC tools and it makes data gathering much simpler.

• To check the shape of the probability distribution of a process
• To quantify defects by type, by location or by cause
• To keep track of the completion of steps in a multistep procedure (as a checklist )
• Tracking the number of defects or errors in a manufacturing process.
• Recording customer complaints or inquiries to identify common issues.
• Monitoring the frequency of equipment breakdowns or maintenance needs.

Provides a structured approach for data collection, making it easier to identify trends, patterns, and areas for improvement.

How to make a checksheet

• Identify the needed information.
• Why do you need to collect the data?
• What type of information should you collect?
• Where should you collect the data from?  
• Who should collect the data?
• When should you collect the data?
• How should you measure the data?
• How much data is essential?

Construct your sheet based on the title, source information and content information (refer to the example below).

Test the sheets. Make sure that all the rows and columns in it are required and relevant and that the sheet is easy to refer to and use. Test it with other collectors and make adjustments based on feedback.

• Quality inspectors or auditors who need to collect data on defects or issues.
• Process operators or technicians responsible for tracking process parameters or measurements.
• Customer service representatives who record customer complaints or inquiries.

Control Chart

The control chart is a type of run chart used to observe and study process variation resulting from a common or special cause over a period of time.

The chart helps measure the variations and visualize it to show whether the change is within an acceptable limit or not. It helps track metrics such as defects, cost per unit, production time, inventory on hand , etc.

Control charts are generally used in manufacturing, process improvement methodologies like Six Sigma and stock trading algorithms.

• To determine whether a process is stable.
• To monitor processes and learn how to improve poor performance.
• To recognize abnormal changes in a process.
• Monitoring the variation in product dimensions during a manufacturing process.
• Tracking the number of customer complaints received per day.
• Monitoring the average response time of a customer support team.

Enables real-time monitoring of process stability, early detection of deviations or abnormalities, and prompt corrective actions to maintain consistent quality.

How to create a control chart

• Gather data on the characteristic of interest.
• Calculate mean and upper/lower control limits.
• Create a graph and plot the collected data.
• Add lines representing the mean and control limits to the graph.
• Look for patterns, trends, or points beyond control limits.
• Determine if the process is in control or out of control.
• Investigate and address causes of out-of-control points.
• Regularly update the chart with new data and analyze for ongoing improvement.
• Production supervisors or operators monitoring process performance on the shop floor.
• Quality control or assurance personnel tracking variation in product quality over time.
• Service managers observing customer satisfaction levels and service performance metrics.

Pareto Chart

The Pareto chart is a combination of a bar graph and a line graph. It helps identify the facts needed to set priorities.

The Pareto chart organizes and presents information in such a way that makes it easier to understand the relative importance of various problems or causes of problems. It comes in the shape of a vertical bar chart and displays the defects in order (from the highest to the lowest) while the line graph shows the cumulative percentage of the defect.

• To identify the relative importance of the causes of a problem.
• To help teams identify the causes that will have the highest impact when solved.
• To easily calculate the impact of a defect on the production.
• Analyzing customer feedback to identify the most common product or service issues.
• Prioritizing improvement efforts based on the frequency of quality incidents.
• Identifying the major causes of delays in project management.

Helps focus improvement efforts on the most significant factors or problems, leading to effective allocation of resources and improved outcomes.

How to create a Pareto chart

• Select the problem for investigation. Also, select a method and time for collecting information. If necessary create a check sheet for recording information.
• Once you have collected the data, go through them and sort them out to calculate the cumulative percentage.
• Draw the graph, bars, cumulative percentage line and add labels (refer to the example below).
• Analyze the chart to identify the vital few problems from the trivial many by using the 80/20 rule . Plan further actions to eliminate the identified defects by finding their root causes.
• Quality managers or improvement teams looking to prioritize improvement initiatives.
• Project managers seeking to identify and address the most critical project risks.
• Sales or marketing teams analyzing customer feedback or product issues.

What’s Your Favorite Out of the 7 Basic Quality Tools?  

You can use these 7 basic quality tools individually or together to effectively investigate processes and identify areas for improvement. According to Ishikawa, it’s important that all employees learn how to use these tools to ensure the achievement of excellent performance throughout the organization.

Got anything to add to our guide? Let us know in the comments section below.

Join over thousands of organizations that use Creately to brainstorm, plan, analyze, and execute their projects successfully.

FAQs about 7 Basic Quality Tools

Quality problems in an organization can manifest in various forms and affect different areas of operations.

• Product defects: Products may have defects or non-conformities that deviate from quality specifications, leading to customer dissatisfaction, returns, or warranty claims.
• Service errors: Service errors can occur when services do not meet customer expectations, such as incorrect billing, delays in delivery, or inadequate customer support.
• Process inefficiencies: Inefficient processes can lead to delays, errors, or rework, resulting in increased costs, decreased productivity, and customer dissatisfaction.
• Poor design or innovation: Inadequate product design or lack of innovation can lead to products that do not meet customer needs, lack competitive features, or have usability issues.
• Supplier quality issues: Poor quality materials or components from suppliers can affect the overall quality of the final product or service.
• Ineffective quality management systems: Inadequate quality management systems, such as lack of quality standards, processes, or documentation, can contribute to quality problems throughout the organization.

The basic quality improvement steps typically follow a systematic approach to identify, analyze, implement, and monitor improvements in processes or products.

• Clearly articulate the problem or identify the area for improvement.
• Collect relevant data and information related to the problem.
• Analyze the collected data to identify patterns, root causes, and opportunities for improvement.
• Brainstorm and generate potential improvement ideas or solutions.
• Assess the feasibility, impact, and effectiveness of the generated improvement ideas.
• Develop an action plan to implement the chosen solution.
• Continuously monitor and measure the results of the implemented solution.
• Based on the monitoring results, evaluate the effectiveness of the implemented solution.
• Once the improvement is successful, document the new processes, best practices, or standard operating procedures (SOPs).
• Iterate through the steps to continuously improve processes and products.

More Related Articles

Amanda Athuraliya is the communication specialist/content writer at Creately, online diagramming and collaboration tool. She is an avid reader, a budding writer and a passionate researcher who loves to write about all kinds of topics.

7 QC Tools | 7 Quality Tools | Process Improvement Tools

7 QC Tools are also known as Seven Basic Quality Tools and Quality Management Tools. These graphical and statistical tools are used to analyze and solve work-related problems effectively.

The 7 Quality Tools are widely applied by many industries for product and process improvements, and to solve critical quality problems.

7QC tools are extensively used in various Problem Solving Techniques which are listed below:

• 8D Problem Solving Methodology.
• PDCA Deming Cycle for Continuous improvement in product and processes.
• Lean Manufacturing for 3M Waste elimination from processes.
• Various phases of Six Sigma-DMAIC to reduce process variations .

Table of Contents

WHAT ARE 7 QC TOOLS?

The 7 quality tools are simple graphical and statistical tools but very powerful in solving quality problems and process improvement.

These statistical tools are very easy to understand and can be implemented without any complex analytical competence or skills.

The 7 tools of quality are generally used by quality control and quality assurance engineers to solve product or process-related quality issues on a daily/weekly/monthly basis and to reduce/eliminate non-value-added activities like product rework, repair, and rejection.

7 QC Tools List | Quality Tools

The list of 7 QC tools are:

Check Sheet

Fishbone diagram, pareto chart, control chart, scatter diagram.

• Stratification Diagram (Some lists replace stratification with  Process Flowchart )

Click on the above links to Explore QC tools.

7 Tools of quality | Brief Explanation

The check sheet is used for collecting, recording, and analyzing the data. Data collection is an important activity in the problem-solving process as it provides a basis for further action. Data may be numerical, observations and opinions, etc.

Fishbone diagram is also called as Cause and Effect diagram and Ishikawa diagram . It helps to Identify all possible potential causes and select the real/best potential cause which contributes to the problem/effect. The brainstorming technique is used for potential cause identification.

In a brainstorming session, all 4M or 6M factors are taken into consideration to identify the potential causes. 4M or 6M factors are – Man, Machine, Method, Material, Measurement, and Mother nature also called Environment.

A Histogram is a pictorial representation of a set of data, and the most commonly used bar graph for showing frequency distributions of data/values. Histogram frequency distribution chart is widely used in Six Sigma problem solving process.

The Pareto chart helps to Narrow the problem area or prioritize the significant problems for corrective measures. The pareto principle is based on the 80-20 rule. It means that 80 percent of the problems/failures are caused by 20 percent of the few major causes/factors which are often referred to as Vital Few .

And the remaining 20 percent of the problems are caused by 80 percent of many minor causes which are referred to as Trivial Many . Hence, it gives us information about Vital few from Trivial many.

A control chart is also known as the SPC chart or Shewhart chart. It is a graphical representation of the collected information/data and it helps to monitor the process centering or process behavior against the specified/set control limits.

A control chart is a very powerful tool to Investigate/disclose the source of Process Variations present in the manufacturing processes. Tells when to take necessary action to eliminate the Common or Random or Chance variations and Special causes of variations.

The control chart helps to measure and analyze the process capability and performance  ( Cp and Cpk and Pp and Ppk ) of the production process.

A Scatter diagram is also known as Correlation Chart, Scatter Plot, and Scatter Graph. A Scatter graph is used to find out the relationship between two variables. In other words, it shows the relationship between two sets of numerical data. Scatter graph shows a Positive or Negative correlation between two variables.

Independent variable data and dependent Variable data are customarily plotted along the horizontal X-axis and Vertical Y-axis respectively. Independent variable is also called controlled parameters.

Stratification Diagram

A technique used to analyze and divide a universe of data into homogeneous groups is called -Strata. Stratification tools are used when the data come from different sources or conditions, such as data collected from different shifts, machines,  people, days,  suppliers and population groups, etc.

Process Flow Chart

A  Process Flow Chart  (PFC) is a diagram of the separate steps of a operations/process in sequential order. PFC is also known as  process flow diagram  (PFD), and Process Map.

WHY DO WE NEED 7 QC TOOLS

We need Quality Tools for :

• Problem Solving – making decisions & judgments.
• For Process Measurement.
• For continual improvement in products, processes, and services.
• To improve Quality , Productivity, and Customer Satisfaction.

“95% of the problem is solved when clearly defined”

“95% of quality-related problems in the organization can be solved by using seven fundamental quantitative tools.”

7QC Tools benefits

The major benefits of QC tools are:

• To analyze and solve quality problems effectively.
• Improve product and process quality .
• Enhance customer satisfaction.
• Reduce cost due to poor quality.
• Helps in investigating the potential causes and real root cause of the problem for taking effective countermeasures.
• Check sheet helps in data collection and recording for quality problem analysis.  
• Identify and reduce the process variation using the SPC quality tool .
• Pareto QC tool helps to narrow down the quality problem using the 80/20 rule.
• Helps in identifying the various sources of variations present in the process.
• Improve the employee’s analytical and problem-solving skills.

You’ll also like:

7 QC TOOLS NEW

The new seven QC Tools are used for planning, goal setting, and problem-solving. These are explained below :

Affinity Diagram – KJ Method. This tool is used for Pinpointing the Problem in a Chaotic Situation and generating solution strategies.

Gathers large amounts of verbal data such as ideas, opinions, issues, and organizes the data into groups based on natural relationships.

Tree Diagram – Also known as Systematic diagram or Dendrograms, Hierarchy diagram, Organisation chart, and Analytical Tree.

This diagram is used for systematically pursuing the best strategies for achieving an objective.

The advantages of the tree diagram are that it facilitates agreement among the team and is extremely convincing with strategies.

Relation Diagram – It is used for cause identification. For finding solutions strategies by clarifying relationships with Complex Interrelated Causes.

Allows for “Multi-directional” thinking rather than linear. Also known as Interrelationship diagrams.

Process Decisions Program Charts (PDPC) – Also called Decision Process Chart. It is used for producing the desired result from many possible outcomes.

The chart is used to plan various contingencies.

PDPC enables problems to pinpoint.

Matrix Diagram – used for Clarifying Problems. It clarifies relationships among different elements.

Matrix Data Analysis – Matrix + Num. Analysis.

This can be used when the Matrix diagram does not give sufficient information.

This is used in various fields like process analysis, new product planning, market surveys, etc.

Arrow Diagram – Gantt Chart + PERT/CPM Chart.

An arrow diagram is employed for understanding optimal schedules and controlling them effectively.

This shows relationships among tasks needed to implement a plan.

This diagram is extensively used in PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method).

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• Seven Quality Tools – Histogram

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Histograms are often used to display the distribution of data. The histogram is shown as a series of vertical bars representing the frequency or relative frequency of data values, with the height of the bar being proportional to the quantity of data it represents.

Histograms are a visual representation of the distribution of data and can show you what is happening with your data across different intervals. Histograms provide an easy way to identify patterns and outliers in data and determine potential problems.

What Is a Histogram?

The histogram is one of the Seven Basic Quality Tools .

A histogram is an easy-to-use tool for visualizing the distribution of data points in a dataset. It can quickly identify outliers, find patterns and spot trends.

What is a Histogram Used for?

Histograms are useful for detecting patterns and trends in data. They also provide insight into the nature of the data. In general, they are good tools for:

• Finding the central tendency of a set of data.

• Spotting outliers.

• Determining whether the data is normally distributed or skewed.

• Finding unusual events.

• Analyzing the variance of a set of data points.

• Detecting anomalies.

• Visualizing large datasets.

What Are the Five Good Features of a Histogram?

The following seven features make a histogram an excellent visualization tool.

1. Easy to Understand and Interpret

You can understand a histogram in just seconds. It's really simple to read and interpret.

2. Quickly Visualized

Because a histogram is simple to create, you can quickly generate it. That makes it easy to spot trends and anomalies.

3. Helps You Detect Trends

When you see a histogram, you usually want to know where the peaks and valleys are located. This helps you detect trends.

4. Helps You Identify Anomalies

An anomaly occurs when a new event takes place. If you look at a histogram, you may notice a spike or dip in one of the bars. This tells you that an event took place in that data range.

5. Great For Large Datasets

Histograms are great for analyzing large datasets because they don't take up much space on the screen. You can easily visualize thousands of data points without having to scroll around.

Tools for creating a histogram

Various tools can be used to create a histogram.

1. Manual: Using a pen and paper: This method can work only if the data is small.

2. Microsoft Excel : This is the most common tool used to create a histogram.

3. Minitab : Minitab is advanced statistical software Six Sigma professionals use. You can draw a histogram using Minitab .

4. Python : Python is a programming language that can be used for many different purposes. It is one of the most popular languages used today for data analysis. You can draw publication quality and professionally looking histograms using Python.

5. R Programming : R is a programming language used for complex statistical analysis. Like Python , you can use R Programming to draw publication quality histograms.

Histograms are a valuable tool in quality management. By using a histogram, you can see accurate data trends, compare groups of data, and identify outliers. These features can help in identifying and quantifying quality issues in a process.

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Histogram Questions

Histogram questions with solutions are provided for students to practise and learn how to interpret histograms. In statistics , a histogram represents a continuous frequency data distribution, whether grouped or ungrouped. By presenting data using a histogram, we represent data points within a particular range or interval. A histogram looks similar to that of a bar graph; the main difference between both of them is that a bar graph is made by keeping uniform gaps in between the rectangular bars, whereas in a histogram, there are no gaps.

Some important facts about histograms:

• Histograms represent a continuous form of data.
• Bars are made with no gaps in between them to show the continuity of the data.
• The height of the bars represents the frequency of the data point, whereas the width represents the length of the class or interval.
• It is required that the calibrations on axes should begin with zero keeping equal intervals. Sometimes, we use a kink or a zig-zag line to show a break in the axes.
• If the chosen class intervals are uniform, then the area of bars directly varies according to the frequency of the class interval.

Learn more facts about histograms and how to make a histogram .

Video Lesson on Histograms

Histograms Questions with Solutions

Let us practice some questions related to plotting and interpreting histograms.

Question 1:

The below histogram shows the weekly wages of workers at a construction site:

Answer the following questions:

(i) How many workers get wages of ₹ 60-70?

(ii) Construct a frequency distribution table.

(iii) What is the cumulative frequency for the class 50-60?

(i) 16 workers

(iii) The cumulative frequency for the class 50-60 = 10 + 20 + 40 = 70.

Question 2:

Study the given histogram:

(i) Prepare a cumulative frequency distribution table for the above histogram.

(ii) Which class interval has the maximum frequency?

(iii) Which class interval has the minimum frequency?

(ii) 10-20 class interval has the maximum frequency.

(ii) 30-40 class interval has the minimum frequency.

Question 3:

The following histogram shows the height of students within a class:

(i) How many students have a height of less than 140 cm?

(ii) How many students have a height greater than 140 cm but less than 155 cm?

(i) Number of students having height less than 140 cm = 6 + 8 + 20 = 34

(ii) Number of students having height greater than 140 cm but less than 155 cm = 18 + 16 = 34.

Question 4:

Study the following histogram and answer the questions given below:

(i) How many students scored below 60%?

(ii) How many students scored above 80%?

(i) Number of students who have scored below 60% = 3 + 2 + 5 = 10

(ii) Number of students who have scored above 80% = 12

Question 5:

The following histogram shows the data regarding the number of people from different age groups who visited to watch an animated movie in a day.

(i) How many people under 20 years of age visited the theatre?

(ii) How many people over 40 years of age visited the theatre?

(i) Number of people under 20 years of age who have visited the theatre = 80 + 140 = 220.

(ii) Number of people over 40 years of age who have visited the theatre = 20.

• Frequency Polygon
• Cumulative Frequency Curve

Question 6:

Draw a histogram for the following data distribution:

The histogram can be plotted as:

Question 7:

Question 8:

Question 9:

Question 10:

The time taken (in seconds) by 25 students to solve a problem was:

17, 20, 24, 26, 27, 30, 38, 34, 40, 35, 47, 41, 44, 49, 45, 48, 44, 54, 50, 60, 58, 58, 63, 55, 20.

Let us make a grouped frequency table for the given data:

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Practice Questions on Histograms

1. Draw a histogram for the following data distribution:

2. Draw a histogram to show the data for rainfall in Madhya Pradesh from 2012 to 2019.

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5 Common Root Cause Analysis Tools for More Effective Problem-Solving

Next to accurately defining a problem, root cause analysis (RCA) is one of the most important elements of problem-solving in quality management. Effective RCA ensures that the actual cause of a problem is identified and addressed, preventing recurrence.

This is where methodologies like Six Sigma, with its DMAIC (Define, Measure, Analyze, Improve, Control) framework, come into play. Six Sigma provides a structured approach that complements RCA tools. It ensures a thorough analysis and sustainable improvement in quality processes.

As you can see, defining the problem is the first step. It’s crucial to identify the right tool for determining the real cause of a problem and prioritizing its solution.

Should you use fault tree analysis, which uses boolean logic, or FMEA, which combines qualitative and quantitative methods? Which is the best root cause analysis tool type for you?

Manufacturers have a range of methods, tools and techniques at their fingertips, each of which is appropriate for different situations. Below, we discuss five common root cause analysis tools:

• Pareto Chart
• Fishbone Diagram
• Scatter Diagram
• Failure Mode and Effects Analysis (FMEA)

Download our free Root Cause Analysis 101 Guidebook

Read 14 quality metrics every executive should know

1. Pareto Chart

A Pareto chart is a histogram or bar chart combined with a line graph that groups the frequency or cost of different problems to show their relative significance. The bars show frequency in descending order, while the line shows cumulative percentage or total as you move from left to right.

The example above is a report from layered process audit software that groups together the top seven categories of failed audit questions for a given facility. Layered process audits (LPAs) allow you to check high-risk processes daily to verify conformance to standards. LPAs identify process variations that cause defects, making Pareto charts a powerful reporting tool for analyzing LPA findings.

These charts are one of the seven basic tools of quality described by quality pioneer Joseph Juran and are based on Pareto’s law, also called the 80/20 rule. This rule says that 20% of inputs drive 80% of results.

Learn how to create Pareto charts in this post or download the Pareto Chart Tip Sheet and Sample Excel File

The 5 Whys is a method that uses a series of questions to drill down into successive layers of a problem. The basic idea is that each time you ask why, the answer becomes the basis of the next why. It’s a simple tool useful for problems where you don’t need advanced statistics, so you don’t necessarily want to use it for complex problems.

One application of this technique is to more deeply analyze the results of a Pareto analysis. Here’s an example of how to use the 5 Whys:

Problem: Final assembly time exceeds the target

• Why is downtime in the final assembly higher than our goal? According to the Pareto chart, the biggest factor is operators needing to constantly adjust Machine A
• Why do operators need to constantly adjust Machine A? Because it keeps having alignment problems
• Why does Machine A keep having alignment problems? Because the seals are worn
• Why are Machine A’s seals worn? Because they aren’t being replaced as part of our preventive maintenance program
• Why aren’t they being replaced as part of our preventive maintenance program? Because seal replacement wasn’t captured in the needs assessment

Of course, it may take asking why more than five times to solve the issue—the point is to peel away surface-level issues to find the root cause of the problem.

Learn more about the 5 Whys method in this blog post or download our free 5 Whys worksheet .

3. Ishikawa Fishbone Diagram

One way to analyze a problem is to draw it out. Being able to see the information organized visually can make it easier to determine the cause and effect of the problem.

A fishbone diagram sorts possible causes into categories that branch off from the original problem. Also called a cause-and-effect or Ishikawa diagram, this tool may have multiple sub-causes branching off each identified category.

The main problem or effect is placed at the “head” of the fish, and the various causes are drawn as “bones” branching off from the main line. These branches are typically grouped into major categories such as People, Methods, Machines, Materials, Measurements, and Environment, though these categories can be customized depending on the specific context.

Each major category can have smaller branches that delve deeper into more specific sub-causes, helping to organize and prioritize potential causes of the problem systematically.

Learn more about how to use a fishbone diagram in this blog post and download our free set of fishbone diagram templates

4. Scatter Plot Diagram

A scatter plot or scatter diagram uses pairs of data points to help uncover relationships between variables. A scatter plot is a quantitative method for determining whether two variables are correlated, such as testing potential causes identified in your fishbone diagram.

Making a scatter diagram is as simple as plotting your independent variable (or suspected cause) on the x-axis, and your dependent variable (the effect) on the y-axis. If the pattern shows a clear line or curve, you know the variables are correlated and you can proceed to regression or correlation analysis.

Download a free tip sheet to start creating your own scatter diagrams today!

5. Failure Mode and Effects Analysis (FMEA)

Failure mode and effects analysis (FMEA) is a method used during product or process design to explore potential defects or failures. An FMEA chart outlines:

• Potential failures, consequences and causes
• Current controls to prevent each type of failure
• Severity (S), occurrence (O) and detection (D) ratings that allow you to calculate a risk priority number (RPN) for determining further action

When applied to process analysis, this method is called process failure mode and effects analysis (PFMEA). Many manufacturers use PFMEA findings to inform questions for process audits , using this problem-solving tool to reduce risk at the source.

No matter which tool you use, root cause analysis is just the beginning of the problem-solving process. Once you know the cause, the next step is implementing a solution and conducting regular checks to ensure you’re holding the gain and achieving sustainable continuous improvement.

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How to Make Histogram Using Analysis ToolPak (with Easy Steps)

In this article, we will demonstrate how to make a histogram using the Analysis Toolpak .

What is a Histogram in Excel?

A histogram is a visual depiction that arranges a number of data points into user-specified intervals, and is structurally identical to a bar chart. But whereas a bar chart compares two variables (X and Y), a histogram only analyzes one variable. The histogram groups several data points into logical ranges or bins in order to reduce a data series into a widely comprehensible graphic.

Create a Histogram Using the Analysis ToolPak (Complete Guideline)

Suppose we have the following sample dataset. Let’s create a histogram from the data.

Step 1 – Setting Up Analysis ToolPak

First, we’ll set up the Analysis ToolPak in Excel.

• Go to the File tab .

• Select the Add-ins tab from the Excel Options dialog box.
• Choose the Analysis ToolPak from the Inactive Application Add-ins .
• Select Excel Add-ins from the Manage drop-down menu.
• Click on the Go… option.

The Add-ins dialog box will appear.

• Choose the Analysis ToolPak from the Add-ins available .

The Data Analysis command is now available in the Data tab’s Analysis set of commands.

Step 2 – Showing the Frequency Table

The list has a total of 18 values ranging between 18 and 65, so we’ll use a bin size of 20 to create the bins. The first bin will therefore range from 0 to 20.

• Enter the top value of this bin, namely 20, into cell C5 .

Data Analysis TookPak requires only the upper value of the bin when making a histogram chart.

• Put the number 30 in cell C6 ( because the next bin has a value greater than 20 and less than or equal to 30).
• Place the 6 upper values in the bins by selecting all the bins for the 18 values in the dataset.

Here is our data table showing the frequency of the data table:

• Go to the Data tab.
• Click on Data Analysis from the Analysis group .

The Data Analysis dialog box will appear.

• Select the Histogram tools.

• Select the Input Range from the above data table.
• Enter the Bin Range from the above data table.
• Choose any cell for the Output Range , for example cell E4 .

We have the frequency table.

Step 3 – Using the Analysis ToolPak to Make a Histogram

The following features will need to be specified to create a Histogram :

Input Range

The dataset’s range will be the input range.

These basically specify what is put into each bar. Care should be taken when choosing these bins. Select the range of bins to input, making sure that the range is in increasing order.

Only check this box if the data ranges are chosen along with the data set header and bin data.

Print Options

Printing the histogram is regulated by these options. By naming a new worksheet, selecting a range in the present worksheet, or choosing a new workbook, the output can be printed.

Print Output Options

What data is shown depends on these choices.

Here is the data table used to make the histogram:

• Click on Data Analysis from the Analysis group.

A Data Analysis dialog box will open.

• Choose the Histogram tool.
• Pick an Input Range from the data table above.
• Enter the Bin Range from the data table above.
• Choose the New Worksheet Ply to see the histogram in another worksheet.
• Choose the Chart Output option.

The final histogram bar chart with the frequency table is as in the below image.

We receive two values between 0 and 20 , six values between 20 and 30 , four values between 30 and 40 , and so on. It is obvious from the figure that there is no pattern to the data.

Read More: How to Use Data Analysis Toolpak in Excel 

Download Practice Workbook

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Kawser Ahmed is a Microsoft Excel Expert, Udemy Course Instructor, Data Analyst, Finance professional, and Chief Editor of ExcelDemy. He is the founder and CEO of SOFTEKO (a software and content marketing company). He has a B.Sc in Electrical and Electronics Engineering. As a Udemy instructor, he offers 8 acclaimed Excel courses, one selected for Udemy Business. A devoted MS Excel enthusiast, Kawser has contributed over 200 articles and reviewed thousands more. His expertise extends to Data Analysis,... Read Full Bio

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