Drawing a histogram with unequal class widths Revision Card

AI generatedStatisticsGCSE Higher / IGCSE Extended

Drawing a histogram with unequal class widths.

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

Draw a histogram for the grouped journey times in minutes.

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 density

Divide each frequency by its own class width.

Use a continuous horizontal scale. Draw each bar between its class boundaries at the calculated density.

Label the horizontal axis with the quantity and units, and the vertical axis “Frequency density”. Adjacent classes meet at their shared boundary.

Example 2

Draw a histogram for the grouped parcel masses in grams.

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 density

Divide each frequency by its own class width.

Use a continuous horizontal scale. Draw each bar between its class boundaries at the calculated density.

Label the horizontal axis with the quantity and units, and the vertical axis “Frequency density”. Adjacent classes meet at their shared boundary.

Your turn

Question 1

Draw a histogram for the grouped leaf lengths in centimetres.

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 density

Divide each frequency by its own class width.

Use a continuous horizontal scale. Draw each bar between its class boundaries at the calculated density.

Label the horizontal axis with the quantity and units, and the vertical axis “Frequency density”. Adjacent classes meet at their shared boundary.

Question 2

Draw a histogram for the grouped journey times in minutes.

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 density

Divide each frequency by its own class width.

Use a continuous horizontal scale. Draw each bar between its class boundaries at the calculated density.

Label the horizontal axis with the quantity and units, and the vertical axis “Frequency density”. Adjacent classes meet at their shared boundary.

Question 3

Draw a histogram for the grouped parcel masses in grams.

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 density

Divide each frequency by its own class width.

Use a continuous horizontal scale. Draw each bar between its class boundaries at the calculated density.

Label the horizontal axis with the quantity and units, and the vertical axis “Frequency density”. Adjacent classes meet at their shared boundary.

Question 4

Draw a histogram for the grouped leaf lengths in centimetres.

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 density

Divide each frequency by its own class width.

Use a continuous horizontal scale. Draw each bar between its class boundaries at the calculated density.

Label the horizontal axis with the quantity and units, and the vertical axis “Frequency density”. Adjacent classes meet at their shared boundary.

Question 5

Draw a histogram for the grouped journey times in minutes.

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 density

Divide each frequency by its own class width.

Use a continuous horizontal scale. Draw each bar between its class boundaries at the calculated density.

Label the horizontal axis with the quantity and units, and the vertical axis “Frequency density”. Adjacent classes meet at their shared boundary.