Histogram

What is a Histogram?

A histogram is used to graphically summarize the distribution of a univariate data set. It shows the spread or the distribution of data that can be measured but not easily categorized. It graphically shows the following:

• center (i.e., the location) of the dat

• spread (i.e., the scale) of the data;

• skewness of the data;

• presence of outliers; and

• presence of multiple modes in the data.

These features provide strong indications of the proper distributional model for the data. 

When to use it?

A histogram can be used to analyze and evaluate the effectiveness of a proposed process change. The histogram is a powerful engineering tool when routinely and intelligently used. The histogram clearly portrays information on location, spread, and shape that enables the user to perceive subtleties regarding the functioning of the physical process that is generating the data. It can also help suggest both the nature of, and possible improvements for, the physical mechanisms at work in the process.

 Examples of Typical Distributions

NORMAL

Ø      Depicted by a bell-shaped curve

Ø      most frequent measurement appears as center of distribution

Ø      less frequent measurements taper gradually at both ends of distribution

Ø      Indicates that a process is running normally (only common causes are present).

BI-MODAL

Ø      Distribution appears to have two peaks

Ø      May indicate that data from more than process are mixed together

Ø      materials may come from two separate vendors

Ø      samples may have come from two separate machines.

CLIFF-LIKE

Ø      Appears to end sharply or abruptly at one end

Ø      Indicates possible sorting or inspection of non-conforming parts.

SAW-TOOTHED

Ø      Also commonly referred to as a comb distribution, appears as an alternating jagged pattern

Ø      Often indicates a measuring problem

Ø      improper gage readings

Ø      gage not sensitive enough for readings.

SKEWED

Ø      Appears as an uneven curve; values seem to taper to one side.

Creating a Histogram

Ø      Determine the range of the data by subtracting the smallest observed measurement from the largest and designate it as R.

1. the largest possible value.

               Largest possible value = 115.9358 minutes  

               Smallest possible value = 89.49606 minutes       

Ø      Record the measurement unit (MU) used.

Ø      Determine the number of classes and the class width. The number of classes, k, should be no lower than six and no higher than fifteen for practical purposes. Trial and error may be done to achieve the best distribution for analysis.

Ø      Determine the class width (H) by dividing the range, R, by the preferred number of classes, k.

Ø      The class width selected should be an odd-numbered multiple of the measurement unit, MU.  This value should be close to the H value:

Ø      Establish the class midpoints and class limits. The first class midpoint should be located near the largest observed measurement. If possible, it should also be a convenient increment. Always make the class widths equal in size, and express the class limits in terms which are one-half unit beyond the accuracy of the original measurement unit. This avoids plotting an observed measurement on a class limit.

Ø      Determine the axes for the graph. The frequency scale on the vertical axis should slightly exceed the largest class frequency, and the measurement scale along the horizontal axis should be at regular intervals which are independent of the class width. (See example below steps.)

Ø      Draw the graph. Mark off the classes, and draw rectangles with heights corresponding to the measurement frequencies in that class.

Ø      Title the histogram. Give an overall title and identify each axis.

Histogram Example

Some important things to remember when constructing a histogram:

Ø      Use intervals of equal length.

Ø      Show the entire vertical axes beginning with zero.

Ø      Do not break either axis.

Ø      Keep a uniform scale across the axis.

Ø      Center the histogram bars at the midpoint of the intervals (in this case, the penetration depth intervals).

Recommended links

• Quality Improvement Tools
• Histogram
• Faq about Quality tools
• Histogram Generator

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