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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 employees
1000150012
150020019
2000250023
2500300024
30003500Y
3500400016
4000450027

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 29

Salary(Rs) No.of employees(fi) (xi) (di=xi1250) fidi
10001500 12 1250 0 12×0=0
15002000 19 1750 500 19×500=9500
20002500 23 2250 1000 23×1000=23000
25003000 24 2750 1500 24×1500=36000
30003500 Y 3250 2000 y×2000=2000y
35004000 16 3750 2500 16×2500=40000
40004500 27 4250 3000 27×3000=81000
Σfi=121+y Σfidi=189500+2000y
Arithmetic mean using direct method formula is ¯¯¯x=a+fixiσfi

a = assumed mean in the above series

¯¯¯x=30.14;a=1250

therefore,

2900=1250+1895002000y121+y

29001250=1895002000y121+y

1650(121+y)=189500+2000y

1650y2000y=189500199650

350y=10150

y=29
Therefore the value of y is 29.

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