Question

The following table gives the literacy rate (in percentage) of $35$cities. Find the mean literacy rate.

Literacy rate (in $\%$)	$45-55$	$55-65$	$65-75$	$75-85$	$85-95$
Number of cities	$3$	$10$	$11$	$8$	$3$

Answer 1

Step - deviation method:

Class Interval	Frequency $\left({\mathrm{f}}_{\mathrm{i}}\right)$	$\left({\mathrm{x}}_{\mathrm{i}}\right)$	${\mathrm{d}}_{\mathrm{i}}={\mathrm{x}}_{\mathrm{i}}–\mathrm{a}$	${\mathrm{u}}_{\mathrm{i}}=\frac{{\mathrm{d}}_{\mathrm{i}}}{\mathrm{h}}$	${\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}$
$45-55$	$3$	$50$	$-20$	$-2$	$-6$
$55-65$	$10$	$60$	$-10$	$-1$	$-10$
$65-75$	$11$	$70$	$0$	$0$	$0$
$75-85$	$8$	$80$	$10$	$1$	$8$
$85-95$	$3$	$90$	$20$	$2$	$6$
	$\sum {\mathrm{f}}_{\mathrm{i}}=35$				$\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}=-2$

The formula to find out the mean is:

Assumed mean($\mathrm{A}$)$=70$

Mean($\mathrm{x̄}$) $=\mathrm{A}+\left(\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}\right)\times \mathrm{h}$

$$\begin{gathered} =70+\left(\frac{-2}{35}\right)\times 10 \\ =70-0.57 \\ =69.42 \end{gathered}$$

Hence, the mean literacy part $=69.42$