Step by step
The question
Question: for the groups 0-10: 4, 10-20: 9, 20-30: 15, 30-40: 8, 40-50: 4, find the median.
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 + 9 = 13, 13 + 15 = 28, 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: 4 at 10, because by 10 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 Median
The median is the middle value.
Half of 40 is 20.
From 20 on the up scale, across to the line, then down: about 24.7.
So the median is about 24.7.
5 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: median.
Last: check.