WAEC Mathematics 2011 Paper

Concept:The modal age is the estimated value corresponding to the tallest bar in the histogram, found using the formula for the mode of grouped data.Explanation:First, identify the tallest bar because it represents the modal class.From the histogram, the lower boundary of this modal class is $L = 40.5$.The class width is $h = 5$.Let $D_1$ be the difference between the modal frequency and the frequency of the previous class.Let $D_2$ be the difference between the modal frequency and the frequency of the following class.The mode formula is:$$\text{Mode} = L + \frac{D_1}{D_1 + D_2} \times h$$Using the frequencies taken from the histogram, the correction term becomes $\frac{D_1}{D_1 + D_2} \times 5 = 2$.Therefore, $\text{Mode} = 40.5 + 2 = 42.5$.Answer:B. $42.5$