Question

Find the median of the given data.
30,32,24,34,26,28,30,35,33,25
A. 32
B. 26
C. 30
D. 25

Answer 1

We here need to find the median of the given data. Median of a data is the middle value of the arranged form of the data. So here, we will first arrange the data in ascending form and then we will see the number of terms of the given data. Then we will use the formula for median given as $\dfrac{\left( \dfrac{{{n}^{th}}\text{ observation}}{2} \right)+\left( \dfrac{{{n}^{th}}\text{ observation}}{2}+1 \right)}{2}$ and hence we will find our required median.

Complete step by step answer:
Median of a scattered data is given as the middle observation of the arranged data.
Here, the numbers given to us are:
30,32,24,34,26,28,30,35,33,25
Now, if we arrange them in ascending order, we will get:
24,25,26,28,30,30,32,33,34,35
Here, we can see that the total number of terms in this data is 10.
Thus, the number of terms in this series is even.
We know that the median of scattered data of ‘n’ number of terms is given by the formula:
$\dfrac{\left( \dfrac{{{n}^{th}}\text{ observation}}{2} \right)+\left( \dfrac{{{n}^{th}}\text{ observation}}{2}+1 \right)}{2}$
As we established above, here n=10.
Thus, putting n=10 in this formula we get:
$\begin{aligned} & Median=\dfrac{\left( \dfrac{{{n}^{th}}\text{ observation}}{2} \right)+\left( \dfrac{{{n}^{th}}\text{ observation}}{2}+1 \right)}{2} \\\ & \Rightarrow Median=\dfrac{\left( \dfrac{{{10}^{th}}\text{ observation}}{2} \right)+\left( \dfrac{{{10}^{th}}\text{ observation}}{2}+1 \right)}{2} \\\ & \Rightarrow Median=\dfrac{{{5}^{th}}\text{ observations}{{6}^{th}}\text{ observation}}{2} \\\ \end{aligned}$
Now, here we can see that,
$\begin{aligned} & {{5}^{th}}\text{ observation=30} \\\ & {{\text{6}}^{th}}\text{ observation=30} \\\ \end{aligned}$
Thus, putting these values here, we get our median as:
$\begin{aligned} & Median=\dfrac{{{5}^{th}}\text{ observations}{{6}^{th}}\text{ observation}}{2} \\\ & \Rightarrow Median=\dfrac{30+30}{2} \\\ & \Rightarrow Median=\dfrac{60}{2} \\\ & \therefore Median=30 \\\ \end{aligned}$
Thus, the median of the given data is 30.

Hence, option (C) is the correct option.

Note:
We have used the formula $\dfrac{\left( \dfrac{{{n}^{th}}\text{ observation}}{2} \right)+\left( \dfrac{{{n}^{th}}\text{ observation}}{2}+1 \right)}{2}$ for calculating the median because here the number of terms is even. But if the number of terms is odd, we have to use a different formula for calculating the median given as $\dfrac{{{\left( n+1 \right)}^{th}}observation}{2}$. Also, we have arranged this data in ascending order but we can arrange it in descending too according to our convenience. It wouldn’t affect our answer.