WAEC Further Mathematics 2016 Paper

Concept:Variance measures the spread of data values around the mean using the average of the squared deviations.Explanation:First, calculate the mean of the given data.$\mu = \frac{11 + 12 + 13 + 14 + 15}{5}$$\mu = \frac{65}{5} = 13$Next, find the deviation of each value from the mean.$11 - 13 = -2$, $12 - 13 = -1$, $13 - 13 = 0$, $14 - 13 = 1$, $15 - 13 = 2$Square each deviation.$(-2)^2 = 4$, $(-1)^2 = 1$, $0^2 = 0$, $1^2 = 1$, $2^2 = 4$Add the squared deviations.$\sum (x - \mu)^2 = 4 + 1 + 0 + 1 + 4 = 10$Now substitute into the variance formula for ungrouped data.$\sigma^{2} = \frac{\sum (x - \mu)^2}{n} = \frac{10}{5}$$\sigma^{2} = 2$Answer:The variance is $2$, which matches option A.