Question 3:
(a) Modal class = time 50 – 54 seconds (highest frequency).
(b)
$$\begin{array}{l}\text{Estimated mean}\\ \text{=}\frac{37\times 5+42\times 8+47\times 9+52\times 15+57\times 11+62\times 2}{50}\\ \text{=}\frac{2475}{50}=49.5\end{array}$$
(c)
(d)
The table below shows the frequency distribution of the time spent by 50 swimmers in the pool in a swimming practice.
Time (seconds) 
Frequency 
35 – 39 
5 
40 – 44 
8 
45 – 49 
9 
50 – 54 
15 
55 – 59 
11 
60 – 64 
2 
(a) State the modal class.
(b) Calculate the estimated mean of the time spent of a swimmer.
(c) Based on table above, complete table below in the answer space by writing down the values of the upper boundary and the cumulative frequency.
Upper Boundary 
Cumulative Frequency 
34.5 
0 
39.5 

64.5 
50 
(d) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 2 cm to 5 seconds on the horizontal axis and 2 cm to 5 swimmers on the vertical axis, draw an ogive for the data.
Solution:(a) Modal class = time 50 – 54 seconds (highest frequency).
(b)
$$\begin{array}{l}\text{Estimated mean}\\ \text{=}\frac{37\times 5+42\times 8+47\times 9+52\times 15+57\times 11+62\times 2}{50}\\ \text{=}\frac{2475}{50}=49.5\end{array}$$
(c)
Upper Boundary 
Cumulative Frequency 
34.5 
0 
39.5 
5 
44.5 
13 
49.5 
22 
54.5 
37 
59.5 
48 
64.5 
50 
(d)