JAMB Mathematics 2023 Paper

Concept:For grouped data, the median is found by locating the class that contains the $\frac{N}{2}$th value and then interpolating within that class.Explanation:Total frequency: $N = 107$.Median position: $\frac{N}{2} = \frac{107}{2} = 53.5$.The cumulative frequency before the median class is $29$.Adding the median class frequency $40$ gives $29 + 40 = 69$, which surpasses $53.5$.Therefore, the median class is "$7 - 8$".Lower boundary: $l_m = 6.5$.Class width: $c = 8.5 - 6.5 = 2$.Frequency of the median class: $f_m = 40$.Cumulative frequency before the median class: $f_b = 29$.Apply the median formula:$$\text{Median} = l_m + \left( \frac{\frac{N}{2} - f_b}{f_m} \right)c$$$$= 6.5 + \left( \frac{53.5 - 29}{40} \right) \times 2$$$$= 6.5 + \left( \frac{24.5}{40} \right) \times 2$$$$= 6.5 + (0.6125 \times 2)$$$$= 6.5 + 1.225$$$$= 7.725$$Answer:The median age of the students is $7.725$ years.Hence, the correct option is A. 7.725.