Percentiles and Quartiles

Percentiles and quartiles are measures of position (or location) in a dataset.
They show how data values are distributed and help you understand where a particular value stands relative to the rest of the data.

In simple terms:

• Percentiles divide your data into 100 equal parts
• Quartiles divide your data into 4 equal parts

Both are used to describe data spread and relative standing within a dataset.

Percentiles

What Is a Percentile?

A percentile indicates the value below which a certain percentage of observations fall.

For example:

• The 25th percentile (P25) is the value below which 25% of the data fall.
• The 50th percentile (P50) is the median — 50% of data are below it.
• The 90th percentile (P90) is the value below which 90% of data fall.

So if your exam score is at the 90th percentile, you scored better than 90% of people.

Example:

Data (ordered): [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]

• P25 (25th percentile) = 25% of 10 = 2.5 → halfway between 2nd and 3rd value
  → (20 + 30)/2 = 25
• P50 (50th percentile) = median = 55
• P75 (75th percentile) = 7.5th position → halfway between 7th and 8th values
  → (70 + 80)/2 = 75

Quartiles

What Are Quartiles?

Quartiles are specific percentiles that divide data into four equal parts:

• Q1 - 25th percentile (P25) - 25% of data are below this value.
• Q2 - 50th percentile (P50) - Median — half the data below, half above.
• Q3 - 75th percentile (P75) - 75% of data are below this value.

Calculating in Python

In NumPy:

import numpy as np​data = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]​q1 = np.quantile(data, 0.25)q2 = np.quantile(data, 0.5)q3 = np.quantile(data, 0.75)​print("Q1 (25th percentile):", q1)print("Q2 (Median, 50th percentile):", q2)print("Q3 (75th percentile):", q3)

In Pandas:

import pandas as pd​data = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]s = pd.Series(data)​q1 = s.quantile(0.25)q2 = s.quantile(0.5)q3 = s.quantile(0.75)​print("Q1:", q1)print("Median (Q2):", q2)print("Q3:", q3)