The following table gives the information of frequency distribution of weekly wages of 150 workers of a company. Find the mean of the weekly wages by 'step deviation' method.

Weekly wages (Rupees)	1000–2000	2000–3000	3000–4000	4000–5000
No. of workers.	25	45	50	30

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: Mean weekly wage ≈ ₹ 3066.67

Take \(A = 2500\) and class width \(h = 1000\).

Class	\(x_i\)	\(d_i = x_i - 2500\)	\(u_i = d_i/1000\)	\(f_i\)	\(f_iu_i\)
1000–2000	1500	-1000	-1	25	-25
2000–3000	2500	0	0	45	0
3000–4000	3500	1000	1	50	50
4000–5000	4500	2000	2	30	60
Total				\(\sum f_i = 150\)	\(\sum f_iu_i = 85\)

\[ \bar{u} = \frac{85}{150} \]

\[ \bar{X} = A + \bar{u}\,h = 2500 + \frac{85}{150} \times 1000 \]

\[ \bar{X} \approx 3066.67 \]

(Taking A = 3500 instead gives the same mean; rounding \(\bar{u}\) to 0.07 gives about ₹ 3070.)

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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