Step by step
The question
Question: for the groups 10-20: 4, 20-30: 8, 30-40: 12, 40-50: 8, 50-60: 8, 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 + 8 = 12, 12 + 12 = 24, and so on, up to 40.
2 Plot at the class ends
Across: the values.
Up: the running total.
The graph starts at 10, with 0: nobody is below the first class.
Each total goes at the END of its class: 4 at 20, because by 20 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 36.7.
So the median is about 36.7.
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.