UPSC CDS Math Statistics Questions

Number of observation = 9 (Odd)
∴ Median =(

n+1

2

)th observation
=(

9+1

2

)th observation
= 5th observation = 20.5
There are 4 observations to the left of the median which are less than 20.5 and 4 observations to the right of the median which are greater than 20.5.
If each of the largest 4 observations of the set is increased by 2, then also the 5th observation would remain 20.5, which is again the median of the new set.
Thus, the median of the new set remains the same as the original set.