Step by step
The question
Question: for the groups 140-150: 4, 150-160: 12, 160-170: 20, 170-180: 10, 180-190: 2, 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: 4, 4 + 12 = 16, 16 + 20 = 36, and so on, up to 48.
2 Plot at the class ends
Across: the values.
Up: the running total.
The graph starts at 140, with 0: nobody is below the first class.
Each total goes at the END of its class: 4 at 150, because by 150 all 4 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: 48 divided by 4 is 12.
From 12 on the up scale, across to the line, then down: about 156.7.
So Q 1 is about 156.7.
The upper quartile is three quarters of the way up: 36.
From 36 on the up scale, across to the line, then down: about 170.
So Q 3 is about 170.
5 Interquartile range
The interquartile range is Q3 minus Q1: about 13.3.
The middle half of the values lies in this range.
6 Check
Let's check: the last running total is 48, 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.