UPSC NDA Math Model Paper 5

For the given data (3, 5, 7, 8, X), the number of observations is n = 5.
Since X ≥ 8, the given observations are already in the ascending order.
Since n = 5 is odd, the median will be the value of the observation a (

5+1

2

)=3rd position.
∴ Median =7
Also, Mean =

3+5+7+8+X

5

.
⇒ Mean =

23+X

5

According to the question:
Median = Mean
⇒7=

23+X

5

⇒35=23+X
⇒X=12