JAMB Mathematics 2011 Paper

Concept:The mode for grouped data is estimated using the modal class, which has the highest frequency.Explanation:The modal class is $6 - 8$ because it has the highest frequency of $5$.Lower class boundary of the modal class: $L_1 = 5.5$.Class width: $C = 8.5 - 5.5 = 3$.$D_1 = 5 - 2 = 3$ (frequency of modal class minus frequency before it).$D_2 = 5 - 3 = 2$ (frequency of modal class minus frequency after it).Now use the mode formula:$$\text{Mode} = L_1 + \left(\frac{D_1}{D_1 + D_2}\right)C$$$$\text{Mode} = 5.5 + \left(\frac{3}{3 + 2}\right)\times 3$$$$\text{Mode} = 5.5 + \frac{3}{5} \times 3$$$$\text{Mode} = 5.5 + \frac{9}{5} = 5.5 + 1.8 = 7.3$$Rounded to the nearest whole number, the mode is approximately $7$.Answer:D. $7$