A continuous grouped frequency distribution consists of four class intervals: 10 - 14, 15 … — JAMB UTME

A continuous grouped frequency distribution consists of four class intervals: $10 - 14$ , $15 - 24$ , $25 - 29$ , and $30 - 44$ . The total frequency of the distribution is $160$ , and the frequency of the class interval $25 - 29$ is $22$ .

In a histogram representing this data, the height of the rectangle for the interval $15 - 24$ corresponds to a frequency density of $6$ . In a pie chart representing the same distribution, the sector angle for the class interval $30 - 44$ is $108^\circ$ .

What is the frequency density of the class interval $10 - 14$ ?

Answer: 6

Answer

The frequency density of the class interval

10 - 14

6

By converting the pie chart sector angle of

108^\circ

into a frequency of

48

out of

160

, and using the frequency density of

6

with class width

10

to find a frequency of

60

for

15 - 24

, the remaining frequency for

10 - 14

30

. Dividing this by the true class width of

5

(from boundaries

9.5

14.5

) gives a frequency density of

6

Step-by-Step Solution

Calculate the frequency of the class interval

30 - 44

from the pie chart sector angle.

Frequency

f_{30-44} = \frac{108^\circ}{360^\circ} \times 160 = 48

The sector angle in a pie chart is directly proportional to the frequency relative to the

360^\circ

total.

Determine the class width and frequency of the class interval

15 - 24

Class boundaries are

14.5

and

24.5

, so width

w = 10

. Frequency

f_{15-24} = 6 \times 10 = 60

Frequency density is defined as frequency divided by class width, so frequency equals frequency density multiplied by class width.

Determine the frequency of the class interval

10 - 14

Frequency

f_{10-14} = 160 - (60 + 22 + 48) = 30

The sum of all class frequencies must equal the total frequency of

160

Calculate the class width and frequency density of

10 - 14

Class width

w_{10-14} = 14.5 - 9.5 = 5

. Frequency density

= \frac{30}{5} = 6

Dividing the frequency of the class (

30

) by its exact class boundary width (

5

) yields the frequency density.

Key Concept

Integration of Frequency Density and Pie Chart Sector Angles

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