Step by step
The question
Question: for the groups 0-30: 12, 30-60: 28, 60-90: 24, 90-120: 16, 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: 12, 12 + 28 = 40, 40 + 24 = 64, and so on, up to 80.
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: 12 at 30, because by 30 all 12 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: 80 divided by 4 is 20.
From 20 on the up scale, across to the line, then down: about 38.6.
So Q 1 is about 38.6.
The upper quartile is three quarters of the way up: 60.
From 60 on the up scale, across to the line, then down: about 85.
So Q 3 is about 85.
5 Interquartile range
The interquartile range is Q3 minus Q1: about 46.4.
The middle half of the values lies in this range.
6 Check
Let's check: the last running total is 80, 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.