# The Manager's Toolkit - Part 6: Plotting for success

## Histograms

Histograms can structure data to make it easier to understand and act upon. Whenever we produce something and measure it, be it in manufacturing or in any other process, the value that is measured will vary over time. One problem we all have is that we make many such measurements and then have a problem with the amount of information that we have. There is an obvious need to structure the information and there is a need for techniques to make the amount of information more manageable. These techniques are known as 'data reduction methods' and histograms are one method for structuring data to make it easier to understand and act upon.

Consider the following measurements:

 20.1 20 19.7 19.4 19.5 19.9 19.3 19.8 19.3 19.4 19.5 19.5 19.6 19.7 19.1 20.2 19.6 19.7 19.0 19.6 19.4 19.2 20.0 19.9 19.8 19.9 19.4 20.1 19.7 19.5 19.6 19.6 20.0 19.8 19.7 20 19.9 19.5 19.4 19.9 19.8 19.5

This data does not tell us a lot and we tend to concentrate on individual numbers and fail to see an overall pattern. Instead of data we want information.

## Tallying information

Histograms are very simple to create and give a quick picture of the information. For the information given above the easiest way to reduce the information would be to use a 'tally sheet' where individual measurements are marked as they are recorded:

## %

19.1

2.4

19.2

2.4

19.3

4.8

19.4

11.9

19.5

14.3

19.6

16.7

19.7

14.3

19.8

9.5

19.9

9.5

20.0

7.1

20.1

4.8

20.2

2.4

Note: When using a tally sheet it is hest to use 'five bar gates' to make recording and later counting easier.

## Plotting a histogram

The real benefit comes when you plot the histogram. The seemingly 'random' data given above can be converted by the tally sheet into a histogram. Which one gives you the most information?

## Example: A Typical Histogram Layout

Value

When the tally sheet is complete, this information can then be plotted as a histogram to help show the big picture clearly and simple. By using a histogram it is easy to see the highest and lowest values, the centre of the distribution, and the chart can give us a 'quick' picture. The interval of the measurements is referred to as the cell size and for the example above the size of the 'cell' was easily seen. In some cases this is more difficult to see and the rules for cell size are as follows:

The cell size can be the same as the unit of measurement but must never be less than this. The unit of measurement is often the best guide to the number of cells, provided the scatter of the results is not too great.

When the unit of measurement is not used then a rough guide for the best number of cells is given by the following rules:

Number of Measurements             Number of Cells

Under 50                                                 5 to 7

50 to 100                                                 6 to10

100 to 250                                               7 to 12

Over250                                                 10 to 20

3) Once the number of cell has been decided an initial estimate of the cell size can be given by the formula:

Cell Size = Highest Measurement - Lowest Measurement
Number of cells

This cell size is then rounded up or down to give a convenient number to plot and use.

Histograms give much more information than either simple measurements or averages. Averages tell you nothing about the best and worst cases or the spread of the results.

## Situations where histograms can be useful:

• To record elapsed time from receipt of order to delivery.

• To determine number of days credit actually given.

• To record results of manufacturing trials etc.

Histograms help to provide the user with a great deal of information, are easily communicated and inexpensively displayed.