Quartile

Definition:

The quartile is a measure of quantile that divides a set of data into four equal parts, called quartiles.

Explanation:

• First Quartile (Q1): The value that 25% of the data falls below.
• Second Quartile (Median): The value that 50% of the data falls below.
• Third Quartile (Q3): The value that 75% of the data falls below.

Formula for Calculating Quartiles:

Q1 = Median - 1 (Q3 - Median)Q3 = Median + 1 (Q3 - Median)

Example:

“`Data: 10, 12, 14, 16, 18, 20, 22, 24, 26

Median = (18 + 20) / 2 = 19

Q1 = 19 – 1 = 18

Q3 = 19 + 1 = 20“`

Applications:

• Comparing quantiles between groups or individuals
• Identifying outliers
• Studying data distribution
• Calculating measures of variability (range, interquartile range)

Notes:

• Quartiles are always ordered in ascending order.
• The median is always the midpoint of the quartile range.
• The range of the quartiles (Q3 – Q1) is called the interquartile range (IQR).
• Quartiles are useful for summarizing and visualizing data distributions.