Question

Calculate the median and third quartile using the following data:
$$\begin{array}{ccccccccc}\text{Mid- Points marks}& 5& 15& 25& 35& 45& 55& 65& 75\\ \text{No. of students}& 3& 10& 17& 7& 6& 4& 2& 1\end{array}$$

Answer 1

The cumulative frequency table for the data is given below.

$$\begin{array}{ccc}\text{Marks}& \text{No. of students}& \text{Cumulative Frequency}\\ X& \left(f\right)& \\ 0-10& 3& 3\\ 10-20& 10& 13\\ 20-30& 17& 30\\ 30-40& 7& 37\\ 40-50& 6& 43\\ 50-60& 4& 47\\ 60-70& 2& 49\\ 70-80& 1& 50\end{array}$$

$\frac{N}{2}=25$
Therefore, median class is 20-30.
Calculation of Median:
$M=L_1+\frac{\frac{N}{2}-c.f}{f}\times cM=20+\frac{25-13}{17}\times 10M=27.05$
Calculation of third quartile:
Class interval of $Q_3=\left(\frac{3N}{4}\right)$th term
$=3\left(\frac{50}{4}\right)$ = 37.5th term
37.5th term corresponds to the class interval 40-50.
$Q_3=L_1+\frac{\frac{3N}{4}-c.f}{f}\times C{Q}_3=40+\frac{37.5-37}{6}\times 10Q_3=40.83$