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

Answer 1

Answer on Question #63554 – 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

There are 8 classes:

Arithmetic mean = $\frac{\sum f x}{\sum f} = \frac{2265}{40} = 56.6$.

ii. Standard deviation

$\bar{x} = 56.6$

Standard deviation = $s = \sqrt{\frac{f(x - \bar{x})^2}{n - 1}} = \sqrt{\frac{5199.37}{40 - 1}} \approx 11.54$

Standard deviation is 11.54.

**Answer:**

i. The arithmetic mean is 56.6.

ii. The standard deviation is 11.54.

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