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)

Estimated mean = 37 × 5 + 42 × 8 + 47 × 9 + 52 × 15 + 57 × 11 + 62 × 2 50 = 2475 50 = 49.5
(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) 

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