Quartile Calculator

Calculate Q1, Q2, Q3 with Step-by-Step Derivation

Enter numbers separated by commas

Quartile Formulas

Q1 = Median of lower half (25th percentile)

Q2 = Median of entire dataset (50th percentile)

Q3 = Median of upper half (75th percentile)

IQR = Q3 - Q1

Quartiles divide data into four equal parts. Q1, Q2 (median), and Q3 help understand data distribution.

⚠ At least 4 values required for meaningful quartile calculation. Results may vary based on method (Tukey, exclusive, inclusive).

What are Quartiles?

Quartiles are values that divide a sorted dataset into four equal parts, each representing 25% of the data.

Q1 (Lower Quartile)

25th percentile. Median of the lower half of data.

Q2 (Median)

50th percentile. Middle value of the dataset.

Q3 (Upper Quartile)

75th percentile. Median of the upper half of data.

Interquartile Range

IQR = Q3 - Q1. Measures middle 50% spread.

💡 Example: Data: 1,2,3,4,5,6,7,8,9. Q1=3, Q2=5, Q3=7, IQR=4.

Applications

Descriptive Statistics Data Analysis Box Plots Outlier Detection Quality Control

Frequently Asked Questions

What are quartiles?▼

Quartiles divide a dataset into four equal parts. Q1 is the 25th percentile, Q2 (median) is the 50th percentile, Q3 is the 75th percentile. They measure data distribution.

How are quartiles calculated?▼

Data is sorted, then Q1 is the median of the lower half, Q2 is the overall median, Q3 is the median of the upper half. Different methods exist (Tukey, Moore & McCabe).

What is the interquartile range (IQR)?▼

IQR = Q3 - Q1. It measures the spread of the middle 50% of data and is resistant to outliers. Used in box plots and outlier detection.

Why are quartiles important?▼

Quartiles describe data distribution, identify central tendency and spread, detect outliers, and are used in descriptive statistics and data visualization.

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