Calculating frequency density Revision Card

AI generatedStatisticsGCSE Higher / IGCSE Extended

Calculating frequency density.

Class width = upper boundary − lower boundary.
Frequency density = frequency ÷ class width; frequency = class width × density.
Histogram bar area represents frequency. Use a continuous horizontal scale and label density on the vertical axis.

Example 1

Calculate the frequency density for each class.

Given journey times in minutes

Class	Frequency
	10
	50
	15
	10

Calculate each width and density

Frequency	Width	Density
10	5	2
50	10	5
15	5	3
10	10	1

Black: given data. Blue: working we add.

First class width

Find the width from the class boundaries.

First density

Frequency density = frequency ÷ class width. Repeat for every row.

Use these densities as the histogram bar heights.

Example 2

Calculate the frequency density for each class.

Given parcel masses in grams

Class	Frequency
	30
	25
	45
	10

Calculate each width and density

Frequency	Width	Density
30	10	3
25	5	5
45	15	3
10	10	1

Black: given data. Blue: working we add.

First class width

Find the width from the class boundaries.

First density

Frequency density = frequency ÷ class width. Repeat for every row.

Use these densities as the histogram bar heights.

Your turn

Question 1

Calculate the frequency density for each class.

Given leaf lengths in centimetres

Class	Frequency
	80
	300
	120
	40

Check answer

Calculate each width and density

Frequency	Width	Density
80	10	8
300	30	10
120	20	6
40	20	2

Black: given data. Blue: working we add.

First class width

Find the width from the class boundaries.

First density

Frequency density = frequency ÷ class width. Repeat for every row.

Use these densities as the histogram bar heights.

Question 2

Calculate the frequency density for each class.

Given journey times in minutes

Class	Frequency
	20
	60
	15
	15

Check answer

Calculate each width and density

Frequency	Width	Density
20	10	2
60	10	6
15	5	3
15	15	1

Black: given data. Blue: working we add.

First class width

Find the width from the class boundaries.

First density

Frequency density = frequency ÷ class width. Repeat for every row.

Use these densities as the histogram bar heights.

Question 3

Calculate the frequency density for each class.

Given parcel masses in grams

Class	Frequency
	15
	60
	15
	10

Check answer

Calculate each width and density

Frequency	Width	Density
15	5	3
60	10	6
15	5	3
10	10	1

Black: given data. Blue: working we add.

First class width

Find the width from the class boundaries.

First density

Frequency density = frequency ÷ class width. Repeat for every row.

Use these densities as the histogram bar heights.

Question 4

Calculate the frequency density for each class.

Given leaf lengths in centimetres

Class	Frequency
	160
	120
	180
	40

Check answer

Calculate each width and density

Frequency	Width	Density
160	20	8
120	10	12
180	30	6
40	20	2

Black: given data. Blue: working we add.

First class width

Find the width from the class boundaries.

First density

Frequency density = frequency ÷ class width. Repeat for every row.

Use these densities as the histogram bar heights.

Question 5

Calculate the frequency density for each class.

Given journey times in minutes

Class	Frequency
	10
	105
	30
	10

Check answer

Calculate each width and density

Frequency	Width	Density
10	5	2
105	15	7
30	10	3
10	10	1

Black: given data. Blue: working we add.

First class width

Find the width from the class boundaries.

First density

Frequency density = frequency ÷ class width. Repeat for every row.

Use these densities as the histogram bar heights.