WAEC Further Mathematics 2012 Paper

Concept:Variance measures the average squared distance of each mark from the mean mark.Explanation:Step 1: Find the mean of the 10 marks.$\overline{x} = \frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10}$$\overline{x} = \frac{55}{10} = 5.5$Step 2: Subtract the mean from each mark and square each difference.The squared deviations are:$6.25,\; 2.25,\; 0.25,\; 12.25,\; 6.25,\; 0.25,\; 12.25,\; 20.25,\; 2.25,\; 20.25$Step 3: Add up all the squared deviations.$\sum (x - \overline{x})^2 = 6.25 + 2.25 + 0.25 + 12.25 + 6.25 + 0.25 + 12.25 + 20.25 + 2.25 + 20.25$$\sum (x - \overline{x})^2 = 82.5$Step 4: Since data for all 10 students is considered, divide by $n = 10$.$\text{Variance} = \frac{\sum (x - \overline{x})^2}{n}$$\text{Variance} = \frac{82.5}{10} = 8.25$Answer:The variance of the marks is $8.25$.Therefore, the correct option is A. 8.25.