It will often be necessary to group the data that you collect, and often you will be asked to work with grouped data.

Grouped data can be described in various ways. It is important that you are able identify the maximum and minimum values that will fit in a particular group, and therefore the width of a group.

The simplest way to define groups, is to state, explicitly, which values go in which group

For Example

Note that each group heading begins with a "greater than or equal to" sign and finishes with a "less than" sign. There is therefore no uncertainty about which group 160 cm falls into.

The minimum value for each group is easy. The smallest value in the first group is 150cm. The maximum value however, is always a cause of argument. We have already said that 160cm belongs in the second group, but this is also taken as the maximum value of the first group.

If we were to be fussy, we could say that the largest number that was less than 160 is

159.9999999999999999999999999999999999999999999999999999999999999999999999999999.....

but if the 9s continue forever, then this is the same as 160. Since we only want the maximum value in order to specify the width of the group, we say that the maximum value is 160, and therefore the width is 10cm. (No-one can argue that each group has a width of 10cm!).

How do we now decide on the maximum and minimum values for each group? Well the values are given as whole numbers, so we need to find the max/min numbers, that when rounded to the nearest whole number fall into the group.

According to the convention for rounding numbers, 159.5 rounds up to 160, but any thing lower (e.g. 159.49999) rounds down to 159, and would therefore belong in the lower group.

Therefore the minimum value of the first group is 149.5cm while the maximum value is taken to be 159.5cm (for the same reason as above.) giving a group width of 10cm.

The groups may not be described to the nearest whole number. For example

In this case the lowest value for the first group would be 0.95 and the maximum value would be taken as 1.45, although a value of 1.45 would be placed in the second group. The width of the first group would therefore be 0.5.

A third way of describing groups, is to just state one boundary, generally the upper boundary.

In this case, any number between 2 and 3 would go in the third group. A value of 3 exactly would go in the third group, but a value of 2 exactly would go in the second group. The width of each group is 1 cm.

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