# Statistics Long Questions (Question 3)

Question 3:
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)

$\begin{array}{l}\text{Estimated mean}\\ \text{=}\frac{37×5+42×8+47×9+52×15+57×11+62×2}{50}\\ \text{=}\frac{2475}{50}=49.5\end{array}$
(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)