Range and Spread

Grade 2

What the range measures

Averages tell you the typical value of a data set. The range tells you how spread out the values are. A small range means the data clusters together; a large range means values vary a lot.

Range = highest value − lowest value

Worked example

EXAMPLE

Two students each sit five tests. Student A scores: 45, 48, 50, 52, 55. Student B scores: 20, 38, 50, 64, 78. Both have a mean of 50. Who is more consistent?

Student A range: 55 − 45 = 10. Student B range: 78 − 20 = 58. Both means are equal, but A has a much smaller range — A's scores are far more consistent. Student A is more consistent.

Comparing data sets

When you compare two data sets, talk about both a measure of average and a measure of spread. Just comparing means often misses the full picture — two data sets can have identical means but completely different ranges.

A typical exam comparison needs two sentences: one about average (who scored higher on average) and one about spread (who was more consistent or reliable).

Limitation of the range

The range depends entirely on the two extreme values. One unusually high or low result changes the range drastically, even if all the other values are tightly bunched together. That's why GCSE also uses the interquartile range — it ignores the extremes.

Try this one

Six numbers have a mean of 9 and a range of 8.

The smallest number is 5.

(a) What is the largest number? [1]

(b) What is the total of all six numbers? [1]

Nova's hint:

Range and mean are two different statistical measures you can use to find missing information.

Ask yourself: 'How is the range calculated from the largest and smallest values, and how does the mean relate to the total?'

Remember: range = largest − smallest, and total = mean × number of values.

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