The median of a set of 9 distinct observations is 20. If each of the l

1.	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» Let the 9 observations be x₁, x₂………..x₉ say Median = (n + 1) / 2 [∵ n = 9 is an odd] = (n + 1) / 2 = 5th term = x₅ = 20 ∴ x₅ = 20 If 2 is added to the last 4 largest numbers then x₁, x₂, x₃, x₄, x₅, x₆ + 2 x₇ + 2, x₈ + 2, x₉ +2 ∴ Median = (n + 1) / 2 = (9 + 1) / 2 = 5th term ∴ x₅ = 20

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»

Let the 9 observations be x₁, x₂………..x₉ say

Median = (n + 1) / 2 [∵ n = 9 is an odd]

= (n + 1) / 2 = 5th term

= x₅ = 20

∴ x₅ = 20

If 2 is added to the last 4 largest numbers then x₁, x₂, x₃, x₄, x₅, x₆ + 2 x₇ + 2, x₈ + 2, x₉ +2

∴ Median = (n + 1) / 2 = (9 + 1) / 2 = 5th term

∴ x₅ = 20