Histogram

A frequency distribution shows how often each different value in a set of data occurs. A histogram is the most commonly used graph to show frequency distributions. It looks very much like a bar chart, but there are important differences between them.

When to Use a Histogram

  • When the data are numerical.
  • When you want to see the shape of the data’s distribution, especially when determining whether the output of a process is distributed approximately normally.
  • When analyzing whether a process can meet the customer’s requirements.
  • When analyzing what the output from a supplier’s process looks like.
  • When seeing whether a process change has occurred from one time period to another.
  • When determining whether the outputs of two or more processes are different.
  • When you wish to communicate the distribution of data quickly and easily to others.

Histogram Construction

  1. Collect at least 50 consecutive data points from a process.
  2. Use the histogram worksheet to set up the histogram. It will help you determine the number of bars, the range of numbers that go into each bar and the labels for the bar edges. After calculating W in step 2 of the worksheet, use your judgment to adjust it to a convenient number. For example, you might decide to round 0.9 to an even 1.0. The value for W must not have more decimal places than the numbers you will be graphing.
  3. Draw x- and y-axes on graph paper. Mark and label the y-axis for counting data values. Mark and label the x-axis with the L values from the worksheet. The spaces between these numbers will be the bars of the histogram. Do not allow for spaces between bars.
  4. For each data point, mark off one count above the appropriate bar with an X or by shading that portion of the bar.

Histogram Analysis

  • Before drawing any conclusions from your histogram, satisfy yourself that the process was operating normally during the time period being studied. If any unusual events affected the process during the time period of the histogram, your analysis of the histogram shape probably cannot be generalized to all time periods.
  • Analyze the meaning of your histogram’s shape.

Typical histogram shapes and what they mean >>

Excerpted from Nancy R. Tague’s The Quality Toolbox, Second Edition, ASQ Quality Press, 2004, pages 292-299.

Create a Histogram

Data Points Histogram* (Excel, 75 KB) – Analyze the frequency distribution of up to 200 data points using this simple, but powerful, histogram generating tool.

Check Sheet Histogram (Excel, 37 KB) – Analyze the number of defects for each day of the week. Start by tracking the defects on the check sheet. The tool will create a histogram using the data you enter.

*Template created by Dean Christolear.

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Read It In QP

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Don’t Leave Learning to ChanceAn exercise helps students of any age understand probability distributions. John C. Howard (Members Only)

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