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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