The interquartile range'

1
The interquartile range.

• A Learning Object produced by
• Sidney Tyrrell, Coventry University,
• as part of her National Teaching Fellowship
  project.

2
The interquartile range

• Quartiles divide the data into quarters.
• 2 3 5 7 10 11 15 16

3
The central quartile is the median

• 2 3 5 7 10 11 15 16

4
Statisticians disagree about how to calculate
exactly where the quartiles lie.

• 2 3 5 7 10 11 15 16

5
But agree that

• quartiles divide the data into quarters.
• 2 3 5 7 10 11 15 16

6
One definition is that

• The lower quartile is the median of the lower
  half of the data set.
• 2 3 5 7 10 11 15 16

The lower quartile is 4
7
With an odd number of numbers

• the lower quartile is the median of the lower
  half of the data below the median itself.
• 2 3 5 7 9 10 11 15 16

The lower quartile is 4
8
The interquartile range

• is the distance between the lower
  quartile and the upper quartile.
• 2 3 5 7 10 11 15 16

9
The interquartile range

• gives the spread of the middle 50 of the data
  often the bit you are most interested in.
• It is not affected by any extreme values.

10
The interquartile range

• Is used in constructing boxplots.
• The quartiles define the ends of the box.

0
20
5
15
10
40
25
30
35
11
Finally a reminder

• Why measure spread?
• Finding the spread helps us understand our data
  better
• which should lead to better decisions and
  analysis.