Question

Answer the following questions in detail−

Calculate Arithmetic mean From the following data Use short-cut method

Wages	10-20	20-30	30-40	40-50	50-60
No. of workers	25	34	40	29	22

Answer 1

Wages	Midpoint xi	f	(X – A) = d	fd
10–20	15	25	–20	–500
20–30	25	34	–10	–340
30–40	(A) 35	40	0	0
40–50	45	29	10	290
50–60	55	22	20	440
		150		–110

$$\begin{gathered} \overline{\mathrm{X}}=\mathrm{A}+\frac{\sum fd}{\mathrm{N}} \\ =35-\frac{110}{150} \\ =34.26 \end{gathered}$$