Question

b) The height of 40 students were measured and recorded as follows;

38.7 40.2 55.4 60.9 70.1 72.5 50.4 63.7
39.4 54.6 59.3 60.2 45.1 66.5 37.9 74.2
44.5 59.6 55.2 60.7 68.0 70.0 71.2 48.3
49.4 54.4 60.9 64.7 69.3 57.4 46.2 68.9
55.3 70.2 71.7 63.2 55.4 39.0 40.3 44.5
Using classes of 35-39, 40-44,- - - calculate;
i. The arithmetic mean
ii. The standard deviation

Answer 1

Answer on Question #63954 – Math – Statistics and Probability

Question

The height of 40 students were measured and recorded as follows:

38.7 40.2 55.4 60.9 70.1 72.5 50.4 63.7

39.4 54.6 59.3 60.2 45.1 66.5 37.9 74.2

44.5 59.6 55.2 60.7 68.0 70.0 71.2 48.3

49.4 54.4 60.9 64.7 69.3 57.4 46.2 68.9

55.3 70.2 71.7 63.2 55.4 39.0 40.3 44.5

Using classes of 35-39, 40-44, calculate:

i. The arithmetic mean

ii. The standard deviation

Solution

i. The arithmetic mean is

$$\bar{x} = \frac{\sum x f}{\sum f} = \frac{2280}{40} = 57.0 \text{ cm}.$$

ii. The standard deviation is

$$s = \sqrt{\frac{\sum x^{2} f - \sum f \cdot (\bar{x})^{2}}{\sum f - 1}} = \sqrt{\frac{135160 - 40 \cdot (57)^{2}}{40 - 1}} = 11.5 \text{ cm}.$$

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