Question

The median of a set of 9 distinct observations is 20. If each of the largest 4 observations of the set is increased by 2, find the median of the resulting set.

Answer 1

Here, the number of observations is 9, which is an odd number.

So, n = 9

Then, Median will be the ${\left(\frac{n+1}{2}\right)}^{th}$ observation

$\Rightarrow {\left(\frac{9+1}{2}\right)}^{th}$ observation = 5th observation = 20

If the terms are arranged in a sorted ascending order, the 4 largest observations will be the 6th, 7th, 8th and the 9th observations.

If these largest 4 observations are increased by 2, it will not affect the median because the median will remain the 5th observation, which is the middlemost term in this set of observations.

So, Median of the resulting set = 20