The following table shows the no. of marks obtained by 41 students of a class: [3 MARKS]
$\begin{array}{ccccccc}Marks& 20& 15& 17& 30& 22& 25\\ obtained& & & & & & \\ Frequency& 10& 2& 5& 4& 12& 8\end{array}$
Find the median of marks obtained

Formula: 1 Mark
Solution: 2 Marks

We arrange the data in ascending order and prepare the cumulative frequency table as given below:

$\begin{array}{ccc}Marksobtained& Frequency& Cumulative\\ & & frequency\\ 15& 2& 2\\ 17& 5& 7\\ 20& 10& 17\\ 22& 12& 29\\ 25& 8& 37\\ 30& 4& 41\end{array}$

Here, n = 41, which is odd
$\therefore$ Median = marks obtained by ${\left(\frac{41+1}{2}\right)}^{th}$ student. = marks obtained by ${21}^{st}$ student.
But, 21 comes corresponding to the cumulative frequency 29 and the term corresponding to the cumulative frequency 29 is 22.
Hence, the median of marks is 22.