          What is it: A Histogram is a basic graphing tool that displays the relative frequency or occurrence of continuous data values showing which values occur most and least frequently. A Histogram illustrates the shape, centering, and spread of data distribution and indicates whether there are any outliers. A graphic way to summarize data. Size is shown on the horizontal axis (in cells) and the frequency of each size is shown on the vertical axis as a bar graph. The length of the bars is proportional to the relative frequencies of the data falling into each cell and the width is the range of the cell. Data is variable measurements from a process.

Why use it: To display variable data so that the pattern of variation can be identified, as this will be shown when the frequency (or distribution) of the items are being measured.

Where to use it:

• 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.

When to use it:

• To help determine if there are special causes of variation present in the process.
• To compare the output of the process with customers’ specifications.

How to use it: 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. The Histogram uses a bar graph of a frequency distribution in which the widths of the bars are proportional to the classes into which the variable has been divided and the heights of the bars are proportional to the class frequencies. Size is shown on the horizontal axis (in cells) and the frequency of each size is shown on the vertical axis as a bar graph. The length of the bars is proportional to the relative frequencies of the data falling into each cell and the width is the range of the cell. Data is variable measurements from a process.

Histogram Construction

• Collect at least 50 consecutive data points from a process.
• Determine the number of bars, the range of numbers that go into each bar and the labels for the bar edges.
• Draw x- and y-axes on the graph. Mark and label the y-axis for counting data values. Mark and label the x-axis with the values for the intervals. The spaces between these numbers will be the bars of the histogram. Do not allow for spaces between bars.
• 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.

#### Important Notes

• A distribution that forms a bell-shaped curve is called a normal distribution.
• The closer the data points fall to the center, the less variation there is in the process. The further away the data points fall from the center, the more variation there is in the process.
• A nearly normal distribution is an indication that the process has mainly common cause variation present.
• A bi-modal or multi-modal distribution is almost always a sign of a special cause of variation in the process or in the data collection technique.
• Points that fall outside of the normal distribution are called outliers and indicate something different than normal has happened in the process. Outliers are important because they send up an immediate red flag that something unusual happened in our process. Whenever we get one of these strange situations, we must immediately find out what caused it and eliminate the cause.

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