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:
Solutions · 1
Official solution
Splitting the 2n observations into a lower half (increased by 5) and upper half (decreased by 3):
Total change =5n−3n=2n
\[\text{New mean} = \frac{\sum x_i+2n}{2n} = \frac{\sum x_i}{2n}+1\]
The mean increases by 1.