Range and Mode

Range

The range is a fairly straightforward thing to calculate; it refers to a set of figures which are often used to calculate an average, but is calculated by finding the difference between the highest and lowest value in the set.

For example, in the following set of figures there are many different values but the range needs you to ignore all but the highest and lowest values.

1, 1, 11, 31, 44, 23, 2, 7, 21, 19, 33, 29, 43, 1, 2, 22, 6, 27, 8

The lowest figure is 1 while the highest figure is 44. The range is the difference between the two, which is 43. The remaining figures do not come into the question at all.

The range is easy to find out when a child is careful and reads all figures. The difficulty may occur when negative numbers are included. Make sure that (s)he remembers that with negative numbers, the larger the number appears, the less its value is. -50 is less than -2, for example. Similarly, when calculating the difference using negative numbers, ensure that the sum takes account of this. The difference between -5 and 2 is 7. If you're not sure about why, check out the negative numbers walkthrough.

Question: What is the range of this set of data?

2, 3, 8, 10, 2, -1, 5, -8, 8, 5, -6, 4

The highest value in this set is 10. The lowest value in the set is -8. The difference between them is (10 - (-8)) = 18.

The range is 18.

Mode

The mode is another easy thing to find once you know what to do. It is tied in with the idea of averages and is usually confused with the mean or the median, with which it is lumped must of the time!

The mode is the most common figure in any given set of data. The word 'mode' is French for 'fashion' and I teach children to associate the two as the only barrier to getting a mark for finding the mode is forgetting which of the three tasks you have to complete. The most fashionable number - the one which is all over the place - the commonest one - these all help a child to see what 'mode' is asking for.

Look at the following set of data and explain what the modal figure is. (N.B. 'modal' is just the adjective formed from the word 'mode'; ensure your child knows this.)

8, 3, 9, 2, 4, 7, 8, 4, 3, 3, 2, 9

There are twelve separate figures here and several get repeated. however, the only digit which turns up more than twice is 3. Therefore it is the modal figure - the one which is the most common.

It really is that easy; however, this information can be used to guide a child to a more complex answer in a problem such as 'if the mode figure is 5, the lowest figure is 3, and the average is 6, what is...'

Make sure that your child counts up more than one set of figures to check that they are right. I've frequently seen children throw away marks through being careless!

Note that it is possible to have more than one modal figure. They do not get averaged out or anything else; simply list them as two separate figures.