(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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) Sector angle represented by the officers:
Total number of officers = 240
Clerks = \(\frac{78}{240} \times 360^\circ = 117^\circ\)
Drivers = \(\frac{36}{240} \times 360^\circ = 54^\circ\)
Typists = \(\frac{44}{240} \times 360^\circ = 66^\circ\)
Messengers = \(\frac{52}{240} \times 360^\circ = 78^\circ\)
Others = \(\frac{30}{240} \times 360^\circ = 45^\circ\)
(b)
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
Mean score = \(\frac{\sum fx}{\sum f}\)
= \(\frac{182}{30}\)
= \(6.067\) marks \(\approxeq\) 6 marks to the nearest whole number.
Source: Myschool Past Questions Archive (Record #54602)