Question

The following frequency distribution shows the daily savings of $64$ children in a locality

Daily savings (in Rs.)	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$	$11-13$	$13-15$
Number of children	$7$	$6$	$x$	$13$	$y$	$5$	$4$

If mean savings is $8$, then find the missing frequencies $x$ and $y$.

Answer 1

Total $=64$children

$7+6+x+13+y+5+4=64x+y=64-9-26x+y=29\to \left(1\right)$

Daily saving average for each

$1-3=2,3-5=4$

So $\frac{2\times 7+64+x6+13\times 8+10\times y+12\times 5+14\times 4}{64}=814+24+6x+104+10y+60+56=8\times 64+6x+10y=512-258$

$6x+10y=2543x+5y=127\to \left(2\right)x+y=29\to \left(1\right)\times 33x+5y=127-3x+3y=87----------2y=40y=20$

So $x=29-20=9x=9$ and $y=20$