Step by step
The question
Question: for the groups 0-20: 8, 20-40: 16, 40-60: 12, 60-80: 4, find the interquartile range.
1 Running total
A table of the groups.
We add a column: the cumulative frequency, the running total.
Each total adds the next frequency on: 8, 8 + 16 = 24, 24 + 12 = 36, and so on, up to 40.
2 Plot at the class ends
Across: the values.
Up: the running total.
The graph starts at 0, with 0: nobody is below the first class.
Each total goes at the END of its class: 8 at 20, because by 20 all 8 have been counted.
Careful!
The running total counts everything up to the end of the class.
So the point goes at the end.
3 Join the points
We join the points from left to right.
4 Quartiles
The lower quartile is a quarter of the way up: 40 divided by 4 is 10.
From 10 on the up scale, across to the line, then down: about 22.5.
So Q 1 is about 22.5.
The upper quartile is three quarters of the way up: 30.
From 30 on the up scale, across to the line, then down: about 50.
So Q 3 is about 50.
5 Interquartile range
The interquartile range is Q3 minus Q1: about 27.5.
The middle half of the values lies in this range.
6 Check
Let's check: the last running total is 40, all the frequencies added.
And the reading is inside its class.
So it fits!
Let's look back.
First: running total.
Then: plot at the class ends.
Then: join the points.
Then: quartiles.
Then: interquartile range.
Last: check.