Eduprobe
Question:
In a set of 2n distinct observations, each of the observations below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then the mean of the new set of observations:
Increases by 1.
Decreases by 1.
Decreases by 2.
Increases by 2.
Solution:
Mean=x1+x2+..+xn+xn+1+..+x2n/2n
Median=(xn+xn+1)/2
New mean=(x1+x2+..+xn+5n+xn+1+..+x2n-3n)/2n
x1+x2+..+xn+xn+1+..+x2n/2n + 2n/2n
New mean=Original mean+1