Question

The lengths of $50$ leaves of a plant are measured corrcct he nearest milimetre and the data obtained is represent in the following table.

Length $\left(mm\right)$	$109-117$	$118-126$	$127-135$	$136-144$	$145-153$	$154-162$	$163-171$
No of leaves	$4$	$6$	$14$	$13$	$6$	$4$	$3$

Answer 1

$Length$ $\left(mm\right)$	$x_i$	$f_i$	$f_i{x}_i$
$108.5-117.5$	$113$	$4$	$452$
$117.5-126.5$	$122$	$6$	$732$
$126.5-135.5$	$131$	$14$	$1834$
$135.5-144.5$	$140$	$13$	$1820$
$144.5-153.5$	$149$	$6$	$894$
$153.5-162.5$	$158$	$4$	$632$
$162.5-171.5$	$167$	$3$	$501$
		$\sum f_i=50$	$\sum f_i{x}_i=6865$

$\Rightarrow$ $Mean\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{6865}{50}=137.3$