Spread

Normal_Distribution.jpgTwo 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.

Range

The range of a set of values is the difference between the highest value and the lowest value.

example

Find the range of 4, 5, 6, 6, 7, 8

Range = 8 − 4 = 4

Quartiles

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

 
LQ
   Median  
UQ
  
1
2
3
5
6
6
7
7
9
9
10
 
3rd value
  
6th value
  
9th value
  

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:

 
LQ
  
Median
  
UQ
  
3
4
5
7
9
(9.5)
10
11
12
13
20
 
3rd value
  
between 5th and 6th value
  

8th value

  

Interquartile Range

The interquartile range of a set of values is the difference between the upper quartile and the lower quartile.

In example 1 above the interquartile range is 9 − 3 = 6

In example 2 above the interquartile range is 12 − 5 = 7

The Working with Data activity provides practice at finding measures of spread.