Question

The ages of the $115$ people who live on an apartment are grouped as follows$:$ The mean length of the plants is $33.43$years using direct method. Find y in the table.

Age(years)	Number of people
$0-10$	$10$
$10-20$	$15$
$20-30$	$26$
$30-40$	Y
$40-50$	$23$
$50-60$	$16$
$60-70$	$3$
$70-80$	$1$

• A. $23$
• B. $28$
• C. $15$
• D. $21$

Answer 1

Answer: (D)

$21$

Length(cm) No. of plants$\left(f_i\right)$ Mid point $x_i$ $f_i{x}_i$

$0-10$ $10$ $5$ $10\times 5=50$

$10-20$ $15$ $15$ $15\times 15=225$

$20-30$ $26$ $25$ $26\times 25=650$

$30-40$ $y$ $35$ $y\times 35=35y$

$40-50$ $23$ $45$ $23\times 45=1035$

$50-60$ $16$ $55$ $16\times 55=880$

$60-70$ $3$ $65$ $3\times 65=195$

$70-80$ $1$ $75$ $1\times 75=75$

$\Sigma f_i=115$ $\Sigma f_i{x}_{=}3110+35y$

Arithmetic mean using direct method formula is

$\overline{x}=\frac{\Sigma f_i{x}_i}{\Sigma f_i}$

$33.43=(3110+35y)/115$

$433.43\times 115=3110+35y$

$3844.45-3110=35y$

$y=734.45/35$

$y=20.9$

Therefore, approximately the value of $y$ is $21.$