The weight (in kg) of 50 contestants at a competition is as follows:
65 66 67 66 64 66 65 63 65 68 64 62 66 64 67 65 64 66 65 67 65 67 66 64 65 64 66 65 64 65 66 65 64 65 63 63 67 65 63 64 66 64 68 65 63 65 64 67 66 64.
(a) Construct a frequenct table for the discrete data.
(b) Calculate, correct to 2 decimal places, the;
(i) mean ; (ii) standard deviation of the data.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Weight (kg)
Frequency
62
1
63
5
64
12
65
14
66
10
67
6
68
2
(b) Using an assumed mean of 65kg
\(x\)
\(f\)
\(fx\)
\(d = x - A\)
\(fd\)
\(fd^{2}\)
62
1
62
-3
-3
9
63
5
315
-2
-10
20
64
12
768
-1
-12
12
65
14
910
0
0
0
66
10
660
1
10
10
67
6
402
2
12
24
68
2
136
3
6
18
\(\sum\) =
50
3253
3
93
(i) Mean \(\bar{x} = \frac{\sum fx}{\sum f}\)
= \(\frac{3253}{50}\)
= 65.06 kg
(ii) \(SD = \sqrt{\frac{\sum fd^{2}}{\sum f} - (\frac{\sum fd^{2}}{\sum f})^{2}}\)
\(SD = \sqrt{\frac{93}{50} - (\frac{3}{50})^{2}}\)
= \(\sqrt{\frac{93}{50} - \frac{9}{2500}}\)
= \(\sqrt{\frac{4650 - 9}{2500}}\)
= \(\sqrt{\frac{4641}{2500}}\)
= \(1.3625 \approxeq 1.36\) (2 d.p.)
Source: Myschool Past Questions Archive (Record #52471)