\(\begin{array}{c|c} \text{Average hourly earnings(N)} & 5 - 9 & 10 - 14 & 15 - 19 & 20 - 24\\ \hline \text{No. of workers} & 17 & 32 & 25 & 24\end{array}\)
Estimate the mode of the above frequency distribution
A. 12.2
B. 12.27
C. 12.9
D. 13.4
Correct Answer: B
Explanation
\(\begin{array}{c|c} \text{Class intervals} & F & \text{Class boundary}\\ \hline 5 - 7 & 17 & 4.5 - 9.5\\ 10 - 14 & 32 & 9.5 - 14.5\\ 15 - 19 & 25 & 14.5 - 19.5\\ 20 - 24 & 24 & 19.5 - 24.5 \end{array}\)
mode = 9 + \(\frac{D_1}{D_2 + D_1}\) x C
= 9.5 + \(\frac{5(32 - 17)}{2(32) - 17 - 25}\)
= 9.5 + \(\frac{75}{27}\)
= 12.27
\(\approx\) 2.3
