Step by step
The question
Question: for the groups 0-20: 5, 20-40: 11, 40-60: 12, 60-80: 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: 5, 5 + 11 = 16, 16 + 12 = 28, and so on, up to 32.
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: 5 at 20, because by 20 all 5 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 32 is 16.
From 16 on the up scale, across to the line, then down: about 40.
So the median is about 40.
5 Check
Let's check: the last running total is 32, 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.