Question

The following table shows the literacy rate (in percent) of 35 cities. Find the mean literacy rate.
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Literacy rate (in \%)} & 45-55 & 55-65 & 65-75 & 75-85 & 85-95 \\ \hline \text{Number of cities} & 3 & 10 & 11 & 8 & 3 \\ \hline \end{array}\]

Hint:

For grouped data with equal class width, use class marks $x_i$ and the formula $\bar{x}=\dfrac{\sum f_i x_i}{\sum f_i}$. A quick check: the mean should lie near the heaviest frequencies (here around $65$--$75$), so $\approx 69%$ makes sense.

Answer 1

Class mark ($x_i$): $50,60,70,80,90$ with frequencies ($f_i$): $3,10,11,8,3$.
Compute $\sum f_i x_i$: $3(50)+10(60)+11(70)+8(80)+3(90)=150+600+770+640+270=2430$.
Total $N=\sum f_i=35$.
\[ \text{Mean}=\bar{x}=\frac{\sum f_i x_i}{\sum f_i}=\frac{2430}{35}=69.428571\ldots \approx \boxed{69.43\%} \]