Practice Statistical measures
Summary statistics such as the mean, median and range describe the centre or spread of a dataset.
The most useful measure depends on the data and the question.
Exercises with solutions
Summary measures condense a data set into a single number. The mean is found by adding all values and dividing by how many there are. The median is the middle value of the sorted list; with an even count you take the mean of the two middle values. The range is the difference between the largest and smallest value.
Exercise 1
Find the mean of 4, 7, 9 and 12.
Show solution and working
8
Sum: 4 + 7 + 9 + 12 = 32. Divide by the count 4: 32 ÷ 4 = 8.
Exercise 2
Find the median of 3, 8, 5, 9, 2.
Show solution and working
5
Sorted: 2, 3, 5, 8, 9. With five values the third is the middle one, so 5.
Exercise 3
Find the median of 4, 10, 6, 8.
Show solution and working
7
Sorted: 4, 6, 8, 10. With four values you take the mean of the two middle ones: (6 + 8) ÷ 2 = 7.
Exercise 4
What is the range of 12, 5, 20 and 8?
Show solution and working
15
The largest value is 20, the smallest 5. The difference is 20 − 5 = 15.
Common mistake
Reading off the median without sorting. Order the list first, then take the middle. Also: the mean can be a value that does not occur in the data at all.
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