WAEC Mathematics

The mean of the numbers 15, 21, 17, 26, 18 and 29 is 21. Calculate the standard deviation.

Correct answer: C

Standard deviation is given by the formula $S = \sqrt{\frac{\sum{(x_i - \overline{x})^2}}{N}}$ where $\overline{x}$ is the average/mean of the numbers and $N$ is the number of numbers we have.

Since $N = 6$ , this means means that

S = \sqrt{\frac{(15-21)^2 + (21-21)^2 + (17-21)^2 + (26-21)^2 + (18-21)^2 + (29-21)^2}{6}} \\ S = \sqrt{\frac{(-6)^2 + 0^2 + (-4)^2 + 5^2 + (-3)^2 + 8^2}{6}} \\ S = \sqrt{\frac{36 + 0 + 16 + 25 + 9 + 64}{6}} \\ S = \sqrt{\frac{150}{6}} = \sqrt{25} \\ S = 5

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The mean of the numbers 15, 21, 17, 26, 18 and 29 is 21. Calculate the standard deviation.

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