Question

If the arithmetic average of date given below be $165$ rupees, find the missing area

Monthly Wages in $\left(Rs\right)$	$100$	$150$	$200$	__	$300$	$500$
Number of Labourers	$30$	$20$	$15$	$10$	$4$	$1$

Answer 1

$x_i$	$f_i$	$x_i\times f_i$
$100$	$30$	$3000$
$150$	$20$	$3000$
$200$	$y$	$3000$
$y$	$10$	$10y$
$300$	$4$	$1200$
$500$	$1$	$500$
	$\sum fi=80$	$\sum f_i{x}_i=10700+10y$

Let Monthly wages $=x_i$

Number of Labourers $=f_i$

Then,

Total no. of Laboureres $=\sum f_i=80$

$\sum f_i{x}_i=10700+10y$

Arthmetic average $\left(\overline{x}\right)=165$

Then,

Arithmetic mean $=\frac{\sum f_i{x}_i}{\sum f_i}$

$165=\frac{10700+10y}{80}$

$165=\frac{10(1070+y)}{80}$

$165=\frac{1070+y}{8}$

$165\times 8=1070+y$

$1320=1070+y$

$1320-1070=y$

$250=y$

The missing area no. is $250$

Hence, this is the answer.