Cumulative frequency: 0-10: 4, 10-20: 9, 20-30: 15, 30-40: 8, 40-50… Easy

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.

▶ Watch it solved

Cumulative frequency: 0-10: 4, 10-20: 9, 20-30: 15, 30-40: 8, 40-50… Medium

The question

Question: for the groups 0-10: 4, 10-20: 9, 20-30: 15, 30-40: 8, 40-50: 4, 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: 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 Quartiles

The lower quartile is a quarter of the way up: 40 divided by 4 is 10.

From 10 on the up scale, across to the line, then down: about 16.7.

So Q 1 is about 16.7.

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: quartiles.

Last: check.

▶ Watch it solved

Cumulative frequency: 0-30: 12, 30-60: 28, 60-90: 24, 90-120: 16… Harder

The question

Question: for the groups 0-30: 12, 30-60: 28, 60-90: 24, 90-120: 16, find the interquartile range.

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: 12, 12 + 28 = 40, 40 + 24 = 64, and so on, up to 80.

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: 12 at 30, because by 30 all 12 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 38.6.

So Q 1 is about 38.6.

The upper quartile is three quarters of the way up: 60.

From 60 on the up scale, across to the line, then down: about 85.

So Q 3 is about 85.

5 Interquartile range

The interquartile range is Q3 minus Q1: about 46.4.

The middle half of the values lies in this range.

6 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.

Then: interquartile range.

Last: check.

▶ Watch it solved