Find the mean daily wages of 50 workers in a factory using the assumed mean method for the following data: Daily Wages (in ₹): 500–520, 520–540, 540–560, 560–580, 580–600 Number of workers: 12, 14, 8, 6, 10

medium 3 marks Class 10 · Mathematics · Statistics

Answer

₹ 545.20

The correct answer is ₹ 545.20 — Apply the mean formula: $\overset{x}{ˉ} = A + \frac{\sum f _{i} d _{i}}{\sum f _{i}} = 550 + \frac{- 240}{50} = 550 - 4.8 = 545.20$ .

Step-by-step solution

Find the class marks ( $x_{i}$ ) for each class interval: $510, 530, 550, 570, 590$ .
Choose an assumed mean $A = 550$ (the middle class mark).
Calculate deviations $d_{i} = x_{i} - A$ : $- 40, - 20, 0, 20, 40$ .
Multiply each frequency $f_{i}$ by its corresponding $d_{i}$ : $12 \times (- 40) = - 480$ , $14 \times (- 20) = - 280$ , $8 \times 0 = 0$ , $6 \times 20 = 120$ , and $10 \times 40 = 400$ .
Sum the frequencies and products: $\sum f_{i} = 50$ and $\sum f_{i} d_{i} = - 480 - 280 + 0 + 120 + 400 = - 240$ .
Apply the mean formula: $\overset{x}{ˉ} = A + \frac{\sum f _{i} d _{i}}{\sum f _{i}} = 550 + \frac{- 240}{50} = 550 - 4.8 = 545.20$ .

Common mistake: Adding negative and positive values of

f_{i} d_{i}

incorrectly.

Concept tested: Assumed mean method for grouped data

Published 28 September 2026 · How this solution was prepared and checked

Find the mean daily wages of 50 workers in a factory using the assumed mean method for the following data: Daily Wages (in ₹): 500–520, 520–540, 540–560, 560–580, 580–600 Number of workers: 12, 14, 8, 6, 10

Step-by-step solution

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