Question

Find the median from the following frequency distribution:

$x$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$f$	$13$	$90$	$81$	$117$	$66$	$27$	$6$	$2$	$2$

Answer 1

Step 1: Make the required frequency distribution table:

At first, we have to prepare a table to find the value of cumulative frequency.

X	F	Cumulative frequency
$3$	$13$	$13$
$4$	$90$	$103$
$5$	$81$	$184$
$6$	$117$	$301$
$7$	$66$	$367$
$8$	$27$	$394$
$9$	$6$	$400$
$10$	$2$	$402$
$11$	$2$	$404$
	$N=404$

Step 3: Calculate the median using the formula for the median of grouped frequency:

The formula for the median will be,

Median$=l+\frac{\frac{N}{2}-F}{f}\times h$

where,

$N=$total observations.

$l=$the lowest limit of the median class.

$f=$frequency of the median class.

$h=$ class size.

$F=$cumulative frequency.of the previous class interval

The lowest limit of the median class$\left(l\right)=6$

Also, $\frac{N}{2}=\frac{404}{2}=202,F=184,h=1,f=117$

Substitute the values on the formula

Median$=6+\frac{202-184}{117}\times 1$

$=6+\frac{18}{117}$

$=6+0.15$

$=6.15$

Median $=6.15$.

Final answer:

Hence, the median value is $6.15$.