Data Science and A.I. : How to Calculate Percentiles Step-by-Step Guide

Numerical Example to Compute Percentile

Given the data set: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, calculate the 30^th and 60^th percentiles.

Percentile

Percentiles are those values of the variate which divide the distribution into 100 equal parts, therefore the number of percentiles is 99.

30^th Percentile

The 30^th percentile is denoted by P₃₀, and to compute its formula is:

P₃₀ = ( ^{30 × (n + 1)} / ₁₀₀ )^th observation

There are 20 observations, so n = 20.

Then,

P₃₀ = ( ^{30 × (20 + 1)} / ₁₀₀ ) = 0.30 × (21 – 1) = 20.10

60^th Percentile

The 60^th percentile is denoted by P₆₀, and to compute it, its formula is:

P₆₀ = ( ^{60 × (n + 1)} / ₁₀₀ )^th observation

Then,

P₆₀ = ( ^{60 × (20 + 1)} / ₁₀₀ ) = 12.60

Observation = 18 + 0.60 × (39 – 36) = 37.20

PDF Presentation

percentiles

Video

 

---