\(\begin{array}{c|c} Class Intervals & 0 - 2 & 3 - 5 & 6 - 8 & 9 - 11 & \\ \hline Frequency & 3 & 2 & 5 & 3 &\end{array}\) Find the mode of the above distribution.
A. 9 B. 8 C. 10 D. 7
Correct Answer: D
Explanation
Mode = L1 + (\(\frac{D_1}{D_1 + D_2}\))C D1 = frequency of modal class - frequency of the class before it D1 = 5 - 2 = 3 D2 = frequency of modal class - frequency of the class that offers it D2 = 5 - 3 = 2 L1 = lower class boundary of the modal class L1 = 5 - 5 C is the class width = 8 - 5.5 = 3 Mode = L1 + (\(\frac{D_1}{D_1 + D_2}\))C = 5.5 + \(\frac{3}{2 + 3}\)C = 5.5 + \(\frac{3}{5}\) x 3 = 5.5 + \(\frac{9}{5}\) = 5.5 + 1.8 = 7.3 \(\approx\) = 7