## What is a Histogram?

A Histogram is a variation of a bar chart in which data values are grouped together and put into different classes. This grouping allows you see how frequently data in each class occur in the data set. Higher bars represent more data values in a class. Lower bars represent fewer data values in a class.

## What Are Histograms Used For?

Histograms are very useful tools for making quality improvements. Since the histogram is such a useful tool, it can have many uses.

- to display large amounts of data values in a relatively simple chart form
- to tell relative frequency of occurrence
- to easily see the distribution of the data
- to see if there is variation in the data
- to make future predictions based on the data

## History of the Histogram

The Histogram was first implemented by Kaoru Ishikawa, one of Japans’ most renowned experts on quality improvement. In 1950, then a member of the Japanese Union of Scientists and Engineers (JUSE), Ishikawa, wanted to make quality control comprehensible to all workers. Inspired by a lecture by Edward Deming, he formalized the *Seven Basic Tools of Quality Control*.

Ishikawa believed that 90% of a company’s problems could be improved using these seven tools, and that –- with the exception of Control Charts — they could easily be taught to any member of the organization. This ease-of-use combined with their graphical nature makes statistical analysis easier for all.

The seven tools are:

**Cause and Effect Diagrams****Pareto Charts****Flow Charts****Check Sheet****Scatter Plots****Control (Run) Chart****Histograms**

## How do Histograms Work?

Histograms are a valuable tool for quality improvement, as long as you know how to use them properly. First, you have to pick a process that you would like to measure. This can be anything from number of items output per week, to the number of calls incoming per day. Basically anything that occurs over an extended period of time. You need to be able to collect at least 100 data values. The more data values, the better. After you collect all of your data, you need to assemble a table of data values. It's important to take into account the frequency of data values.

The next part in using a Histogram is to calculate some statistics so you can make a chart. You need to calculate the mean, minimum, maximum, standard deviation, class width, number of classes, skewness, and kurtosis.

Mean is the average of all values. Minimum is the smallest value. Maximum is the biggest value. Standard Deviation is how widely spread the values are around the mean. Class Width is the x-axis distance between the left and right edges of each bar in the histogram. Number of Classes is the number of bars in the Histogram. Skewness is the alignment of the Histogram. Kurtosis is a measure of the "peakness" of the distribution. After you calculate these statistics, you can create the actual histogram – it will take one of five following shapes:

- normal distribution
- positively skewed
- negatively skewed
- bi-modal distribution
- multi-modal distribution

## Shapes of Distributions

## Histograms For Analysis

After completing the Histogram, its use as a tool for quality improvement can be seen. You can look at the completed histogram and analyze its shape. Along with the statistics that you calculated, you can get a good idea of where any problems might be, or where to make any changes to the process.

This exercise on the web allows the user to see all of the important parts of a Histogram. The user can be walked through the making of the histogram, this allows the user to better understand what a Histogram is all about, and how it can be applied to real life quality problem.