Question

Compute the median from the following data:

Marks Obtained	$0-7$	$7-14$	$14-21$	$21-28$	$28-35$	$35-42$	$42-49$
Number of Students	$3$	$4$	$7$	$11$	$0$	$16$	$9$

Answer 1

Step 1: Construct the cumulative frequency table.

Marks Obtained	Number of Students	Cumulative Frequency
$0-7$	$3$	$3$
$7-14$	$4$	$7$
$14-21$	$7$	$14$
$21-28$	$11$	$25$
$28-35$	$0$	$25$
$35-42$	$16$	$41$
$42-49$	$9$	$50$

Step 2: Determine the median class.

$N=\sum _{}f=50$

$\therefore \frac{N}{2}=\frac{50}{2}=25$

The cumulative frequency just greater than $25$ is $41$ and the corresponding class is $35-42$.

Hence, the median class is $35-42$.

Step 3: Calculate the median.

The median for grouped data when class intervals are given is,

$\mathrm{Median}=l+\left(\frac{{\displaystyle \frac{N}{2}}-cf}{f}\right)\times h$

Here,

$l$ is the lower limit of the median class, i.e., $l=35$

$\frac{N}{2}=25$

$cf$ is the cumulative frequency of the class preceding the median class i.e., $cf=25$

$f$ is the frequency of the median class i.e., $f=16$

$h$ is the class size i.e., $h=7$

Substitute the above values in the formula for the median.

$\begin{array}{rcl}\mathrm{Median}& =& 35+\left(\frac{{\displaystyle 25-25}}{16}\right)\times 7\\ & =& 35+0\\ & =& 35\end{array}$

Hence, the median for the given data is $35$.