WAEC Mathematics 2013 Paper

Concept:The mode of a grouped distribution is estimated from the modal class using its boundaries and the frequencies of neighbouring classes.Explanation:From the given histogram, the tallest bar shows the modal class as $50.5$ to $55.5$.So, the lower class boundary is $L = 50.5$ and the class width is $h = 5$.The frequency of the modal class is $f_m = 10$.The frequency of the class just before it is $f_{m-1} = 7$.The frequency of the class just after it is $f_{m+1} = 8$.For grouped data, the mode is calculated by:$$\text{Mode} = L + \frac{f_m - f_{m-1}}{(f_m - f_{m-1}) + (f_m - f_{m+1})} \times h$$Substitute the values:$$\text{Mode} = 50.5 + \frac{10 - 7}{(10 - 7) + (10 - 8)} \times 5$$$$\text{Mode} = 50.5 + \frac{3}{3 + 2} \times 5$$$$\text{Mode} = 50.5 + \frac{3}{5} \times 5 = 50.5 + 3 = 53.5$$Answer:C. $53.5$