## Comparing Data

There are two types of statistic al graphs which are useful for recording and then comparing more than one set of data.

The stem and leaf graph which allows easy recording and display of data in order, and box and whisker diagrams, which clearly show the spread of different sets of data.

### Stem and Leaf Diagram

A stem and leaf diagram or chart provides a means of ordering and displaying data and comparing two sets of data.

Numbers are split into categories of the first digit(s) and the last digits(s)

e.g. Given the following test scores:

06, 24, 43, 23, 12, 34, 21, 08, 15, 47, 40, 20, 12, 05, 19, 28, 34, 23, 39, 34

Let the stem be the first digit (the tens column). Now enter each of the second digits (the units column) into the leaf part of the diagram.

 0 6 8 5 1 2 5 2 9 2 4 3 1 0 8 3 3 4 4 9 4 4 3 7 0

Now arrange the leaf digits in order.

 0 5 6 8 1 2 2 5 9 2 0 1 3 3 4 8 3 4 4 4 9 4 0 3 7

Both parts of a stem and leaf diagram can contain more than one digit.

e.g. For numbers such as 3476, the stem could be 34 and the leaf could be 76.

### Back to Back Stem and Leaf Diagrams

This type of stem and leaf diagram is good for comparing two samples or sets of data.

e.g. A class's scores in tests out of 50

 English Mathematics 6 0 7 9 8 5 3 1 1 1 2 2 4 6 1 4 6 7 9 2 3 5 6 8 9 9 2 4 5 8 3 1 4 7 3 5 6 4 3 4 5 0 Units of stem is 10 marks

The way that each set of marks are distributed can be seen clearly on this type of diagram.

### Box and Whisker Graphs

Box and whisker graphs are useful for comparing the data in different frequency distributions.

The diagrams consist of a rectangle which indicates the quartiles and the median, and a line on each end to show the maximum and minimum values of the distribution.

e.g. Draw a box and whisker diagram to compare the following frequency distributions of two schools' mathematics examinations results.

School A: Median, 51; Lower quartile, 42; Upper quartile, 65; Maximum, 95; Minimum, 23

School B: Median, 54; Lower quartile, 39; Upper quartile, 68; Maximum, 99; Minimum, 15 From the diagram above, the two sets of marks can now be compared.

School B would appear to have the higher marks with a higher median, upper quartile and maximum.

School A's results are less spread, with an interquartile range of 23, compared to School B's 29.