Statistics Normal Distribution

statistics normal distribution business slide

Statistics normal distribution is a description of how data is shaped when plotted on a frequency diagram or a histogram . Normal distribution is the most common shape of data. Above is a histogram of a data set that has normal distribution.

This Data Analysis Video teaches you the basic tools for understanding, summarizing, and making future predictions with your collected data. Includes MS Excel templates.

Data Analysis Video

Statistics Normal Distribution Described

With normal distribution, most of the data is in the center. As you get further away from the average, the less frequent the data appears. I drew a curve on the graph. This curve is called a bell shape curve because it looks like a musical bell. Normal distribution possesses the bell shape curve. Normal distribution will also be called bell shaped data.

The average of the data will be in the center. In some cases you will have perfect normal distribution. In this case the median = mode = mean .

You can use Microsoft Excel to create Histograms.

My First Normal Distribution

The first time I encountered normal distribution was during high school. I remember the teacher telling me that the grades would be based on the curve. I asked myself, what is this curve she speaks of? That curve was the bell shape curve or normal distribution. From my grades perspective, I just didn’t want to be on the beginning side of the curve.

Little did I know at that time, the importance of that curve. That curve represents natural variation. The bell shape curve appears everywhere. In about 90% of all data you collect meets normal distribution. Normal distribution is responsible for about 95% of all applied statistics.

This Data Analysis Video teaches you the basic tools for understanding, summarizing, and making future predictions with your collected data. Includes MS Excel templates.

Data Analysis Video

Statistics Normal Distribution

When you have a Normal Distribution, you can apply statistics and make predictions about the data set. These statistics allows you to describe your data set in terms of averages and standard deviation.

In addition you can apply process control tools such as SPC when you have normal distribution.

Below is a normal distribution curve that is separated by 1, 2, and 3 standard deviations from the center.

99% of the data occur within +/- 3 standard deviations. You can use the below chart to see the percentage of data with each standard deviation.

If you have specifications you can conduct a process capability study on data sets with normal distribution. Quality Assurance relies on collecting data. That data needs to be studied and understood. Statistical normal distribution lets you do both.

Creating a Histogram


One of the Total Quality Management Tools is the Histogram.

One uses this graph to show frequency distributions. It looks very much like a bar chart.

When to Use:

This chart graphs data distributions. If you have numerical, variable, continuous data you can use the this chart. The chart organizes and sorts the data. It shows the data in a pictorial format.

Construction :

Collect at least 50 data points from a process.

Use the worksheet below to set up the chart. It helps you determine the number of bars, the width of the bar, and the labels for the bar edges.

After calculating width in step 2 of the worksheet, use your judgment and adjust it to a convenient round number. For example, you might decide to round 0.9 to an even 1.0. The value for W may not have more decimal places than any number in your data set.

Draw x- and y-axes on graph paper. Mark and label the y-axis for counting the data values. Mark and label the x-axis with the L values from the worksheet. The spaces between these numbers will create the bars. Do not allow for spaces between bars.

For each data point, locate it where it fits within the Ls. Mark off one count above the appropriate bar with an X or by shading that portion of the bar.


Consider this simple example. Below shows the exam results collected from a training class of 50 individuals:

Below is the chart. The center of the data shows about 69. The average is probably near 69. Construct these bar charts to provide a useful picture of your data.

Comment Box is loading comments...

More Info

  • Data and Information

    Data and Information, are often used interchangeably, they don’t mean the same thing

  • Process Improvement and KPOVs

    Lean Sigma is different to many traditional Process Improvement initiatives in its reliance on data to make decisions

  • Histogram in Excel

    Follow these steps to create a Histogram in Excel. This includes turning on data analysis, creating bins, and sorting data.

  • Histogram Examples: A Picture of Your Data

    See our histogram examples. We discuss normal distribution and how it applies to quality assurance. Histograms are a key process improvement tool.

  • Learn Data Analysis Techniques

    When you understand data analysis techniques, you take a big step towards making product and process improvements.

  • Data Analysis Video

    Download Today. Don’t take chances without understanding your data. Data drives business decisions. But how does this work? This introduction to Data Analysis Video shows you how to gather, summarize, and present data to management and your team. $69.00. Satisfaction guaranteed.

  • Run Chart

    A Run Chart displays the process performance over time. It is a line graph of data points plotted in chronological order. Learn more!

  • Regression

    See our article on regression, includes details, collecting the data, examples, roadmap and possible problems

  • Data analysis in excel

    Data analysis in excel discusses calculating averages, ranges, and standard deviation in Microsoft Excel.

  • Continuous Data

    Learn how to evaluate your continuous data and assure satisfactory inspection. Without conducting an MSA on your data set, you put your inspection data at risk.

  • Process Capability Studies

    Process capability studies demonstrate the fit of your data to your specifications. Machine process capability determines current and future defects.

  • Chi Square

    Learn how to apply Chi Square in practice, when to use it , how to insure results

Quality Assurance Solutions
Robert Broughton
(805) 419-3344
Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.

All Products

Software, Videos, Manuals, On-Line Certifications

PDCA Complete

An Organizational Task Management System. Projects, Meetings, Audits & more

8D Manager

Corrective Action Software

TrainingKeeper Software

Plan and Track Training

Snap Sampling Plans!

AQL Inspection Software

QAS Business Slide Deck

450+ Editable Slides with support links


Learn and Train TRIZ

ISO 9001:2015 QA Manual

Editable Template

ISO 9001:2015 QMS Kit

Templates, Guides, QA Manual, Audit Checklists

ISO 14001:2015 EMS Kit

EMS Manual, Procedures, Forms, Examples, Audits, Videos

On-Line Accredited Certifications

Six Sigma, Risk Management, SCRUM

All Products

Software, Videos, Manuals, On-Line Certifications