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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


Answer :

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

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