Question

What is the median for the following observations?
$5,8,6,9,11,4$
A. $6$
B. $7$
C. $8$
D. None of these

Answer 1

Hint: Median of a distribution is the value of the observation which divides the distribution into two equal parts. If the values in the ungrouped data are arranged in order of increasing or decreasing magnitude, then the median is the value of the middlemost observation. Also we should look whether the number of observations are even or odd because it creates a difference in the answer. In this given data, the number of terms are even, therefore,
Median $ = $Value of ${(\dfrac{n}{2})^{th}}$observation + Value of ${(\dfrac{n}{2} + 1)^{th}}$observation $2$

Complete step-by-step answer:
Given observations are $5,8,6,9,11,4$
Arranging the given data in ascending order, we get $4,5,6,8,9,11$.
Here, the number of observations $ = 6$, which is even ($n = 6$).
Therefore, we apply the formula of median, where the number of terms are even,
Median $ = $Value of ${(\dfrac{n}{2})^{th}}$observation + Value of ${(\dfrac{n}{2} + 1)^{th}}$observation $2$
$\Rightarrow $Median $ = $Value of ${(\dfrac{6}{2})^{th}}$observation + Value of ${(\dfrac{6}{2} + 1)^{th}}$observation $2$
$\Rightarrow $Median $ = $Value of ${3^{^{rd}}}$observation + Value of ${4^{th}}$observation $2$
On substituting the values in the above expression, we get
$\Rightarrow $Median $ = \dfrac{{6 + 8}}{2} = 7$
Therefore, we get the median of the given observations as $7$.
Hence, Option B is the correct choice.

Note: Median is referred to as the middle most value of a series.
If the number of terms are even, then,
Median $ = $Value of ${(\dfrac{n}{2})^{th}}$observation + Value of ${(\dfrac{n}{2} + 1)^{th}}$observation $2$
If the number of observations are odd, then,
Median $ = $ Value of ${(\dfrac{{n + 1}}{2})^{th}}$observation $2$