Question

The following data gives the distribution of height of students
$\begin{array}{cccccccc}Hight\left(incm\right)& 160& 150& 152& 161& 156& 154& 155\\ Numberofstudents& 12& 8& 4& 4& 3& 3& 7\end{array}$
The median of the distribution is

• A. 154
• B. 155
• C. 160
• D. 161

Answer 1

The correct option is B 155

Arranging the data in ascending order of magnitude, we obtain
$\begin{array}{cccccccc}Hight\left(incm\right)& 150& 152& 154& 155& 156& 160& 161\\ Numberofstudents& 8& 4& 3& 7& 3& 12& 14\\ Cumulativefrequency& 8& 12& 15& 22& 25& 37& 41\end{array}$
Here total number of items is 41 i.e., an odd number.
Hence, the median is $\frac{41+1}{2}$th i.e., ${21}^{st}$ item.
From cumulative frequency table we find that median i.e., ${21}^{st}$ item is $155.$