WAEC Mathematics 2017 Paper

Concept:Variance measures the average of the squared differences from the mean.Explanation:First, find the mean of the data.$\text{Mean} = \frac{2+3+3+4+5+5+5+7+7+9}{10} = \frac{50}{10} = 5$Now calculate each squared deviation from the mean.$(2-5)^2 = 9$$(3-5)^2 = 4$, and this appears twice, giving $2 \times 4 = 8$$(4-5)^2 = 1$$(5-5)^2 = 0$, and this appears three times$(7-5)^2 = 4$, and this appears twice, giving $2 \times 4 = 8$$(9-5)^2 = 16$Add all squared deviations: $9 + 8 + 1 + 0 + 8 + 16 = 42$Number of observations, $N = 10$Variance $= \frac{\text{Sum of squared deviations}}{N} = \frac{42}{10} = 4.2$Answer:Variance $= 4.2$, so the correct option is D.