Consider the following distribution of daily wages of 50 workers of a factory.

Daily wages (in Rs.)	100-120	120-140	140-160	160-180	180-200
Number of workers	12	14	8	6	10

Find the mean daily wages of the workers of the factory by using an appropriate method.

The midpoint of the given interval is found by formula: \(Midpoint \ (x_i) \ = \ \frac{upper \ limit \ + \ lower \ limit}{2} \)

In this case, the value of mid-point ( \(x_i\)) is very large,so let us assume the mean value, A = 150 and class interval is h = 20.

So, \(u_i \ = \ \frac{x_i \ - \ A}{h} \ \)
\( \Rightarrow\ u_i \ = \ \frac{x_i \ - \ 150}{20} \)

So, the formula to find out the mean is : \( \ \overline{x} \ = \ A \ + h \frac{ \sum \ f_i x_i}{ \sum f_i} \)
\( = \ 150 \ + \ 20 \ × \ \frac{-12}{50} \)
\(= \ 150 \ - \ 4.8 \)
\(= \ 145.20 \)
\(\therefore \) Mean daily wage of the workers = Rs. 145.20