Recovering total frequency from an unlabelled histogram scale Revision Card

AI generatedStatisticsGCSE Higher / IGCSE Extended

Recovering total frequency from an unlabelled histogram scale.

Use a known class to calibrate the scale: density = frequency ÷ class width.
Divide its density by the number of vertical grid spaces to find the scale per space.
Frequency = width × density. Use each class’s own width; add frequencies to find total.

Example 1

The class has frequency 15. Find the total frequency. The density scale is unlabelled.

Calibrate the scale and add the bar areas

Class	Width	Density	Frequency
	5	2	10
	10	5	50
	5	3	15
	10	1	10
Total			85

Black: given data. Blue: working we add.

Known density

Use the supplied frequency and the matching class width.

This is the density represented by one vertical grid space.

Total frequency

For each bar, multiply its width by its density, then add the frequencies.

Example 2

The class has frequency 10. Find the total frequency. The density scale is unlabelled.

Calibrate the scale and add the bar areas

Class	Width	Density	Frequency
	10	3	30
	5	5	25
	15	3	45
	10	1	10
Total			110

Black: given data. Blue: working we add.

Known density

Use the supplied frequency and the matching class width.

This is the density represented by one vertical grid space.

Total frequency

For each bar, multiply its width by its density, then add the frequencies.

Your turn

Question 1

The class has frequency 80. Find the total frequency. The density scale is unlabelled.

Check answer

Calibrate the scale and add the bar areas

Class	Width	Density	Frequency
	10	8	80
	30	10	300
	20	6	120
	20	2	40
Total			540

Black: given data. Blue: working we add.

Known density

Use the supplied frequency and the matching class width.

This is the density represented by one vertical grid space.

Total frequency

For each bar, multiply its width by its density, then add the frequencies.

Question 2

The class has frequency 60. Find the total frequency. The density scale is unlabelled.

Check answer

Calibrate the scale and add the bar areas

Class	Width	Density	Frequency
	10	2	20
	10	6	60
	5	3	15
	15	1	15
Total			110

Black: given data. Blue: working we add.

Known density

Use the supplied frequency and the matching class width.

This is the density represented by one vertical grid space.

Total frequency

For each bar, multiply its width by its density, then add the frequencies.

Question 3

The class has frequency 15. Find the total frequency. The density scale is unlabelled.

Check answer

Calibrate the scale and add the bar areas

Class	Width	Density	Frequency
	5	3	15
	10	6	60
	5	3	15
	10	1	10
Total			100

Black: given data. Blue: working we add.

Known density

Use the supplied frequency and the matching class width.

This is the density represented by one vertical grid space.

Total frequency

For each bar, multiply its width by its density, then add the frequencies.

Question 4

The class has frequency 40. Find the total frequency. The density scale is unlabelled.

Check answer

Calibrate the scale and add the bar areas

Class	Width	Density	Frequency
	20	8	160
	10	12	120
	30	6	180
	20	2	40
Total			500

Black: given data. Blue: working we add.

Known density

Use the supplied frequency and the matching class width.

This is the density represented by one vertical grid space.

Total frequency

For each bar, multiply its width by its density, then add the frequencies.

Question 5

The class has frequency 10. Find the total frequency. The density scale is unlabelled.

Check answer

Calibrate the scale and add the bar areas

Class	Width	Density	Frequency
	5	2	10
	15	7	105
	10	3	30
	10	1	10
Total			155

Black: given data. Blue: working we add.

Known density

Use the supplied frequency and the matching class width.

This is the density represented by one vertical grid space.

Total frequency

For each bar, multiply its width by its density, then add the frequencies.