Question

Find the mean of the following frequency distribution:

Class	$101-110$	$111-120$	$121-130$	$131-140$	$141-150$	$151-160$
Frequency	$11$	$16$	$20$	$30$	$14$	$9$

Answer 1

Class Interval	Mean Value $\left(x\right)$	Frequency $\left(f\right)$	$f\times x$
$101-110$	$105.5$	$11$	$1160.5$
$111-120$	$115.5$	$16$	$1848$
$121-130$	$125.5$	$20$	$2510$
$131-140$	$135.5$	$30$	$4065$
$141-150$	$145.5$	$14$	$2037$
$151-160$	$155.5$	$9$	$1399.5$
		$\Sigma f=100$	$\Sigma fx=13020$

Mean, $\overline{x}=\frac{\Sigma fx}{\Sigma f}$

$\Rightarrow \overline{x}=\frac{13020}{100}$

$\Rightarrow \overline{x}=130.2$

Hence, the mean is $130.2$.