Question

Let X be the sample median of uniform random variables. Find a good numerical approximation for the 75th percentile of the distribution of X.

Answer 1

P₇₅ = (3/2) X

Explanation:

Given

The median m = P₅₀ = X

P₇₅ = ?

Knowing that

P₅₀ = X = n*50/100

where n is the number of data points

If

X = n*50/100 ⇒ n = 2X

then we apply the formula

P₇₅ = n*75/100

⇒ P₇₅ = (2X)*75/100

⇒ P₇₅ = (3/2) X