Range is a measure of the spread of data. It is the difference between the largest and the smallest values. It is used, for example, in looking at the results of a test, to see what range of the available marks has been achieved. To find the range of a set of data, take the smallest value from the largest value.
Example one
In a set of tests, two pupils scored the following marks out of 10:
John: 5, 6, 4, 5, 5, 6, 5, 7
Sally: 3, 2, 3, 6, 5, 8, 6, 9
The lowest mark John scored is 4 and the highest mark he scored is 7, so the range of John's marks is 3 (from 4 to 7).
Sally's marks are between 2 and 9 making the range for Sally's marks 7.
From this we can see that Sally's marks are more widely spread than John's marks. John's marks are fairly consistent, whereas Sally obtains some high and some low marks.
Example two
The marks scored by a group of pupils in an end of term test marked out of 80 are as follows.
37, 45, 53, 61, 70, 50, 48, 29, 52, 59
The teacher was interested in the spread of marks. What is the range of the set of marks?
The lowest mark is 29
The highest mark is 70
The difference: 70 - 29 = 41
The range of marks is 41. This result shows wide variation in the group's performance on this test.
Example three
The scatter graph shows the percentage scores of a group of pupils in test A and test B. Each dot on the graph represents one pupil. So pupil X scored 58 in test A and 48 in test B. Pupils' scores might be plotted on a scatter graph to see whether there is a correlation between the marks on the two tests. It shows that pupil P scored well in both tests, but that pupil M scored well on test A but badly on test B. The range helps in the analyses of tests to see to what extent they distinguish between the high achieving and low achieving pupils.
Which test (A or B) had the greater range?
To find the range of marks in test A, look along the x axis (horizontal) and read off the first and last values.
The lowest percentage score for test A is 49.
The highest percentage score for test A is 80.
The range of percentage scores for test A is 80 - 49 = 31.
To find the range of scores in for test B, look up the y axis (vertical) and read off the first and last values.
The lowest percentage score for test B is 10.
The highest percentage score for test B is 81.
The range of percentage scores for test B is 81 - 10 = 71.
Test A percentage range is 31.
Test B percentage range is 71.
The greater range is test B.
So in test B, a wider range of percentage scores were obtained.