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
$1000-1500$	$12$
$1500-200$	$19$
$2000-2500$	$23$
$2500-3000$	$24$
$3000-3500$	Y
$3500-4000$	$16$
$4000-4500$	$27$

• A. $27$
• B. $28$
• C. $29$
• D. $30$

Answer 1

Answer: (C)

$29$

Salary(Rs) No.of employees$\left(f_i\right)$ $\left(x_i\right)$ $(d_i=x_i-1250)$ $f_i{d}_i$

$1000-1500$ $12$ $1250$ $0$ $12\times 0=0$

$1500-2000$ $19$ $1750$ $500$ $19\times 500=9500$

$2000-2500$ $23$ $2250$ $1000$ $23\times 1000=23000$

$2500-3000$ $24$ $2750$ $1500$ $24\times 1500=36000$

$3000-3500$ $Y$ $3250$ $2000$ $y\times 2000=2000y$

$3500-4000$ $16$ $3750$ $2500$ $16\times 2500=40000$

$4000-4500$ $27$ $4250$ $3000$ $27\times 3000=81000$

$\Sigma f_i=121+y$ $\Sigma f_i{d}_i=189500+2000y$

Arithmetic mean using direct method formula is $\overline{x}=a+\frac{\sim f_i{x}_i}{\sigma f_i}$

a = assumed mean in the above series

$\overline{x}=30.14;a=1250$

therefore,

$2900=1250+\frac{189500-2000y}{121+y}$

$2900-1250=\frac{189500-2000y}{121+y}$

$1650(121+y)=189500+2000y$

$1650y-2000y=189500-199650$

$-350y=-10150$

y$=29$

Therefore the value of y is $29.$