Step by step
The question
Question: for the groups 20-40: 10, 40-60: 30, 60-80: 25, 80-100: 15, find the lower quartile.
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: 10, 10 + 30 = 40, 40 + 25 = 65, and so on, up to 80.
2 Plot at the class ends
Across: the values.
Up: the running total.
The graph starts at 20, with 0: nobody is below the first class.
Each total goes at the END of its class: 10 at 40, because by 40 all 10 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 46.7.
So Q 1 is about 46.7.
5 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.
Last: check.