Question

The median of a set of 9 distinct observations is 20.5. If each of the observations of a set is increased by 2, then the median of a new set ______.

पर्याय

• is increased by 2

• is decreased by 2

• is two times the original number

• remains same as that of original observations

Answer 1

The median of a set of 9 distinct observations is 20.5. If each of the observations of a set is increased by 2, then the median of a new set is increased by 2.

Explanation:

Given that we have 9 distinct observations.

Let 9 distinct observations in ascending order be x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈ and x₉.

Now, let’s assume that n is an odd number.

Median = `((9 + 1)/2)^("th") "term"`

= 5^th term

Also, the median is given as 20.5.

Thus, 5^th term = x₅ = 20.5

Now, each observation is increased by 2.

Therefore, the new observations are x₁ + 2, x₂ + 2, x₃ + 2, x₄ + 2, x₅ + 2, x₆ + 2, x₇ + 2, x₈ + 2 and x₉ + 2.

Since all observations have increased, our ascending order remains the same.

Thus, the new median will be the new 5^th term.

New median = New 5^th term

= x₅ + 2

= 20.5 + 2

= 22.5

Thus, the new median is increased by 2.