Cumulative frequency: 0-10: 6, 10-20: 10, 20-30: 4, find the median

Step by step

The question

Question: for the groups 0-10: 6, 10-20: 10, 20-30: 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: 6, 6 + 10 = 16, 16 + 4 = 20, and so on, up to 20.

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: 6 at 10, because by 10 all 6 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 20 is 10.

From 10 on the up scale, across to the line, then down: about 14.

So the median is about 14.

5 Check

Let's check: the last running total is 20, 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.