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# 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 85-98 Number of cities 3 10 11 8 3

In this case, the value of mid-point (xi) is very large,

so let us assume the mean value, A = 70 and class interval is h = 10.

So, $$u_i \ = \ \frac{x_i \ - \ A}{h}$$

$$=> \ u_i \ = \ \frac{x_i \ - \ 70}{10}$$

 Class Interval Frequency $$(f_i)$$ $$(x_i)$$ $$d_i \ = \ x_i \ - \ A$$ $$u_i \ = \ \frac{d_i}{h}$$ $$f_i u_i$$ 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 $$\sum f_i \ = \ 35$$ $$\sum f_i u_i \ = \ -2$$

So,

$$\overline{x} \ = \ A \ + h \frac{ \sum \ f_i x_i}{ \sum f_i}$$

$$= \ 70 \ + \ \frac{-2}{35} \ × \ 10$$

$$= \ 69.42$$

$$\therefore$$ The mean literacy part is 69.42