Question

The value of houses in a particular area are shown in the table.

Value per house (in lakhs)	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Number of houses	$12$	Y	$5$	$8$	$3$

Given the mean value of the houses is $30.14$lakhs. and assumed mean is $35$

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (A)

$7$

Value per house(in lakhs) Number of houses$\left(f_i\right)$ $\left(x_i\right)$ $(d_i-x_i-35)$ $f_i{d}_i$

$10-20$ $12$ $15$ $-20$ $112\times -20=-240$

$20-30$

$Y$ $25$ $-10$ $y\times 10=-10y$

$30-40$ $5$ $35$ $0$ $5\times 0=0$

$40-50$ $8$ $45$ $10$ $8\times 10=80$

$50-60$ $3$ $55$ $20$ $3\times 20=60$

$\Sigma f_i=28+y$ $\Sigma f_i{d}_i=-100-10y$

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

a = assumed mean in the above series

$\overline{x}=30.14;a=35;$

Therefore,

$30.14=35+\frac{-100-10y}{28+y}$

$30.14-35=\frac{-100-10y}{28+y}$

$-4.86(28+y)=-100-10y$

$-136.08+100=-10y+4.86y$

$y=-36.08/-5.24=6.88$

Approximately the value of y is $7$.