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.
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.
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Correct Answer: Option n
Explanation:
(a)
(b) Using an assumed mean of 65kg
(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.)
(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.)