(a) The distribution of junior workers in an institution is as follows: Clerks - 78, Drivers - 36, Typists - 44, Messengers - 52, Others - 30. Represent the...
Question 1 Report
(a) The distribution of junior workers in an institution is as follows: Clerks - 78, Drivers - 36, Typists - 44, Messengers - 52, Others - 30. Represent the above information by a pie chart.
(b) The table below shows the frequency distribution of marks scored by 30 candidates in an aptitude test.
| Marks | 4 | 5 | 6 | 7 | 8 | 9 |
| No of candidates | 5 | 8 | 5 | 6 | 4 | 2 |
Find the mean score to the nearest whole number.
Answer Details
(a) Pie chart of junior workers
First find the total number of workers:
\[ 78+36+44+52+30 = 240 \]The angle of each sector is a fraction of the whole circle \(\left(360^\circ\right)\):
\[ \text{Sector angle} = \frac{\text{Number in category}}{240}\times 360^\circ \]| Category | Number | Sector angle |
|---|---|---|
| Clerks | 78 | \(\frac{78}{240}\times360^\circ=117^\circ\) |
| Drivers | 36 | \(\frac{36}{240}\times360^\circ=54^\circ\) |
| Typists | 44 | \(\frac{44}{240}\times360^\circ=66^\circ\) |
| Messengers | 52 | \(\frac{52}{240}\times360^\circ=78^\circ\) |
| Others | 30 | \(\frac{30}{240}\times360^\circ=45^\circ\) |
| Total | 240 | \(360^\circ\) |
The five sector angles add up to \(117^\circ+54^\circ+66^\circ+78^\circ+45^\circ=360^\circ\), confirming the calculation. Drawn to scale with a protractor, the pie chart is:
(b) Mean score of the aptitude test
Multiply each mark \(x\) by its frequency \(f\) to obtain \(fx\):
| Marks \((x)\) | 4 | 5 | 6 | 7 | 8 | 9 | Total |
|---|---|---|---|---|---|---|---|
| No. of candidates \((f)\) | 5 | 8 | 5 | 6 | 4 | 2 | 30 |
| \(fx\) | 20 | 40 | 30 | 42 | 32 | 18 | 182 |
To the nearest whole number, the mean score is 6 marks.
Download The App On Google Playstore
Everything you need to excel in your exams
