Question

Find the medion of 66,98,54,92,87,63,72.

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

$\text{The median of the Given data is 72}$

$\textbf{\underline{\underline{Explanation :-}}}$

$\star$What is Median ??

• When the data is arranged in the Ascending or Descending order, the middle observation is said to be the Median.

Arrange the data in Ascending or Descending order.

Ascending order =

54 , 63 , 66 , 72 , 87 , 92 , 98

Median of odd Observation =

Value of ${\tt{\dfrac{(n+1)}{2}^{th}}}$

= value of ${\tt{\dfrac{(7+1)}{2}^{th}}}$

= 4 th Observation

Value of 4th Observation

= 72

Middle Observation = 72

$\therefore$$\text{The median of the Given data is 72}$

⟩⟩ $\textbf{\underline{\underline{Extra Info}}}$ ⟨⟨

$\star$How to find Median ??

$\textbf{Case I}$: If there are odd number of observations.

If there are odd number of observations,the Median is the middle observation.

Example : There are 5 observations

12 ,15 , 17 , 19, 21

Median will be the third Observation,

Median = 17

In general we can say that if the number of Observation (n) are odd then the Median will be the $\tt{{\left(\dfrac{n + 1}{2}\right)^{th}}}$ Observation.

$\textbf{Case II}$ : When there are even number of Observations

If there are even number of Observations the Median will be the mean of the two Central Observations.

Example :

If there are 6 Observations 12 , 15 , 17 , 18 , 19 and 21.

Then the Median will be mean of 3rd and 4th Observation i.e.

Average of 17 (3rd Observation)and

18 (4th Observation)

Median =

$\tt{\implies \dfrac{17 + 18}{2} }$

$\tt{\implies \: \dfrac{35}{2} }$

$\tt{\implies17.5}$

In general we can say that the number of Observation (n) is even,

Then the Median will be the mean of $\tt{\left( \dfrac{n}{2} + 1\right) ^{th}}$Observation.