Two sets of data can have a similar mean, mode and median but contain completely different values.
e.g. 4, 5, 6, 6, 7, 8 and 1, 6, 6, 11, 12.
The mean, median and mode for both sets of data is 6 but the second set of numbers is much more spread out than the first.
The spread of a set of data can be measured using the range or the quartiles.
The range of a set of values is the difference between the highest value and the lowest value.
The median is the value which splits a set of values into two equal parts.
The quartiles split a set of values into four equal parts.
The lower quartile (LQ or Q1) is the value below which one quarter of the values lie.
The upper quartile (UQ or Q3 ) is the value below which three quarters of the values lie.
Finding the quartiles
For a set of data with an odd number of values:
Example 1 For the 11 values: 1 ,2, 3, 5, 6, 6, 7, 7, 9, 9, 10
For a set of data with an even number of values:
Example 2 For the 10 values: 3, 4, 5, 7, 9, 10, 11, 12, 13, 20:
The interquartile range of a set of values is the difference between the upper quartile and the lower quartile.
The Working with Data activity provides practice at finding measures of spread.