 # Frequency Densities

In this worksheet, students calculate frequency densities from class width and frequencies shown in data tables. Key stage:  KS 4

Curriculum topic:  Statistics

Curriculum subtopic:  Interpret and Construct Tables and Line Graphs for Time Series Data

Difficulty level:   ### QUESTION 1 of 10

 Frequency density  = frequency width of class interval

Example

A company has 725 workers.

The following table shows the distribution of weekly wages.

Weekly Wages (£) frequency (f)
0 ≤ w < 200 200
200 ≤ w < 300 200
300 ≤ w < 350 125
350 ≤ w < 500 150
500 ≤ w < 600 50
Total 725

Work out the Frequency Densities for this distribution.

We extend the table with two new columns to show class width and Frequency density.

Using the formula below, we work out the Frequency density for each class width.

 Frequency density  = frequency width of class interval

Weekly Wages (£) frequency (f) Class width Frequency density
0 ≤ w < 200 200 200   200 ÷ 200 = 1
200 ≤ w < 300 200 100   200 ÷ 100 = 2
300 ≤ w < 350 125 50   125 ÷ 50 = 2.5
350 ≤ w < 500 150 150   150 ÷ 150 = 1
500 ≤ w < 600 50 100   50 ÷ 100 = 0.5
Total  725

A company has 900 workers.

The following table shows the distribution of weekly wages.

Weekly Wages (£) frequency (f)
0 ≤ w < 200 200
200 ≤ w < 300 400
300 ≤ w < 350 100
350 ≤ w < 500 150
500 ≤ w < 600 50
Total 900

Work out the Frequency Density for the 300 ≤ w < 350 class interval.

A company has 900 workers.

The following table shows the distribution of weekly wages.

Weekly Wages (£) frequency (f)
0 ≤ w < 200 200
200 ≤ w < 300 400
300 ≤ w < 350 100
350 ≤ w < 500 150
500 ≤ w < 600 50
Total 900

Work out the Frequency Density for the 200 ≤ w < 300 class interval.

A company has 900 workers.

The following table shows the distribution of weekly wages.

Weekly Wages (£) frequency (f)
0 ≤ w < 200 200
200 ≤ w < 300 350
300 ≤ w < 350 100
350 ≤ w < 500 200
500 ≤ w < 600 50
Total 900

Work out the Frequency Density for the 500 ≤ w < 600 class interval.

The heights of 100 plants are measured.

The following table shows the distribution of heights.

Height (cm) frequency (f)
0 ≤ h < 20 20
20 ≤ h < 25 35
25 ≤ h < 35 20
35 ≤ h < 45 20
45 ≤ h < 60 5
Total 100

Work out the Frequency Density for the 0 ≤ h < 20 class interval.

The heights of 100 plants are measured.

The following table shows the distribution of heights.

Height (cm) frequency (f)
0 ≤ h < 20 20
20 ≤ h < 25 35
25 ≤ h < 35 20
35 ≤ h < 45 20
45 ≤ h < 60 5
Total 100

Work out the Frequency Density for the 25 ≤ h < 35 class interval.

The heights of 100 plants are measured.

The following table shows the distribution of heights.

Height (cm) frequency (f)
0 ≤ h < 20 20
20 ≤ h < 25 35
25 ≤ h < 35 20
35 ≤ h < 45 20
45 ≤ h < 60 5
Total 100

Work out the Frequency Density for the 20 ≤ h < 25 class interval.

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 5 ≤ a < 10 class interval.

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 10 ≤ a < 16 class interval.

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 16 ≤ a < 18 class interval.

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 18 ≤ a < 30 class interval.

• Question 1

A company has 900 workers.

The following table shows the distribution of weekly wages.

Weekly Wages (£) frequency (f)
0 ≤ w < 200 200
200 ≤ w < 300 400
300 ≤ w < 350 100
350 ≤ w < 500 150
500 ≤ w < 600 50
Total 900

Work out the Frequency Density for the 300 ≤ w < 350 class interval.

2
EDDIE SAYS
Class width = 350 - 300 = 50
Frequency Density = 100 ÷ 50 = 2
• Question 2

A company has 900 workers.

The following table shows the distribution of weekly wages.

Weekly Wages (£) frequency (f)
0 ≤ w < 200 200
200 ≤ w < 300 400
300 ≤ w < 350 100
350 ≤ w < 500 150
500 ≤ w < 600 50
Total 900

Work out the Frequency Density for the 200 ≤ w < 300 class interval.

4
EDDIE SAYS
Class width = 300 - 200 = 100
Frequency Density = 400 ÷ 100 = 4
• Question 3

A company has 900 workers.

The following table shows the distribution of weekly wages.

Weekly Wages (£) frequency (f)
0 ≤ w < 200 200
200 ≤ w < 300 350
300 ≤ w < 350 100
350 ≤ w < 500 200
500 ≤ w < 600 50
Total 900

Work out the Frequency Density for the 500 ≤ w < 600 class interval.

0.5
EDDIE SAYS
Class width = 600 - 500 = 100
Frequency Density = 50 ÷ 100 = 0.5
• Question 4

The heights of 100 plants are measured.

The following table shows the distribution of heights.

Height (cm) frequency (f)
0 ≤ h < 20 20
20 ≤ h < 25 35
25 ≤ h < 35 20
35 ≤ h < 45 20
45 ≤ h < 60 5
Total 100

Work out the Frequency Density for the 0 ≤ h < 20 class interval.

1
EDDIE SAYS
Class width = 20 - 0 = 20
Frequency Density = 20 ÷ 20 = 1
• Question 5

The heights of 100 plants are measured.

The following table shows the distribution of heights.

Height (cm) frequency (f)
0 ≤ h < 20 20
20 ≤ h < 25 35
25 ≤ h < 35 20
35 ≤ h < 45 20
45 ≤ h < 60 5
Total 100

Work out the Frequency Density for the 25 ≤ h < 35 class interval.

2
EDDIE SAYS
Class width = 35 - 25 = 10
Frequency Density = 20 ÷ 10 = 2
• Question 6

The heights of 100 plants are measured.

The following table shows the distribution of heights.

Height (cm) frequency (f)
0 ≤ h < 20 20
20 ≤ h < 25 35
25 ≤ h < 35 20
35 ≤ h < 45 20
45 ≤ h < 60 5
Total 100

Work out the Frequency Density for the 20 ≤ h < 25 class interval.

7
EDDIE SAYS
Class width = 25 - 20 = 5
Frequency Density = 35 ÷ 5 = 7
• Question 7

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 5 ≤ a < 10 class interval.

3
EDDIE SAYS
Class width = 10 - 5 = 5
Frequency Density = 15 ÷ 5 = 3
• Question 8

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 10 ≤ a < 16 class interval.

4
EDDIE SAYS
Class width = 16 - 10 = 6
Frequency Density = 24 ÷ 6 = 4
• Question 9

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 16 ≤ a < 18 class interval.

19
EDDIE SAYS
Class width = 18 - 16 = 2
Frequency Density = 38 ÷ 2 = 19
• Question 10

The ages of 100 young people attending a holiday club are recorded.

The following table shows the distribution of ages.

Age (years) frequency (f)
0 < a < 5 5
5 ≤ a < 10 15
10 ≤ a < 16 24
16 ≤ a < 18 38
18 ≤ a < 30 18
Total 100

Work out the Frequency Density for the 18 ≤ a < 30 class interval.

1.5
EDDIE SAYS
Class width = 30 - 18 = 12
Frequency Density = 18 ÷ 12 = 1.5
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