WAEC Mathematics 2020 Paper

Concept:Standard deviation measures the average distance of each data value from its mean.Explanation:The given mean is $\bar{x} = 21$, so we use this mean to find the deviations.The deviations $(x - \bar{x})$ for $15, 21, 17, 26, 18, 29$ are $-6, 0, -4, 5, -3, 8$.Square each deviation to get: $36, 0, 16, 25, 9, 64$.Add these squared deviations: $\sum (x - \bar{x})^2 = 36 + 0 + 16 + 25 + 9 + 64 = 150$.There are $n = 6$ values in the data set.Apply the standard deviation formula: $\sigma = \sqrt{\frac{\sum (x - \bar{x})^2}{n}}$.Substitute the values: $\sigma = \sqrt{\frac{150}{6}} = \sqrt{25}$.Therefore, $\sigma = 5$.Answer:The standard deviation is $5$.