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Question

# The weekly salaries of employees in railway department are as follows. Given the mean salaries is 2900 Rs. and assumed mean is 1250.Salary(Rs)Number of employees1000−1500121500−200192000−2500232500−3000243000−3500Y3500−4000164000−450027

A
27
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B
28
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C
29
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D
30
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Solution

## The correct option is D 29Salary(Rs) No.of employees(fi) (xi) (di=xi−1250) fidi1000−1500 12 1250 0 12×0=01500−2000 19 1750 500 19×500=95002000−2500 23 2250 1000 23×1000=230002500−3000 24 2750 1500 24×1500=360003000−3500 Y 3250 2000 y×2000=2000y3500−4000 16 3750 2500 16×2500=400004000−4500 27 4250 3000 27×3000=81000Σfi=121+y Σfidi=189500+2000y Arithmetic mean using direct method formula is ¯¯¯x=a+∼fixiσfia = assumed mean in the above series¯¯¯x=30.14;a=1250therefore,2900=1250+189500−2000y121+y2900−1250=189500−2000y121+y1650(121+y)=189500+2000y1650y−2000y=189500−199650−350y=−10150 y=29Therefore the value of y is 29.

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