Quartile Calculator

Quartile Calculator

Calculate quartiles (Q0, Q1, Q2, Q3, Q4), interquartile range, and analyze data distribution by percentiles.

Last updated: March 2026

Dataset Input

Q0 (Min)
6.00
Q1 (25th)
25.50
Q2 (Med)
40.00
Q3 (75th)
42.50
Q4 (Max)
49.00
Key Metrics
IQR (Q3 - Q1)17.000
Sample size11
Sorted Data
6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49

What are Quartiles?

Quartiles divide a sorted dataset into four equal parts. They show where the 25th, 50th, and 75th percentiles fall, giving you insight into data spread and distribution.

Q1 (25th percentile): 25% of data is below this value. Q2 (50th percentile/median): 50% of data is below this. Q3 (75th percentile): 75% of data is below this. The interquartile range (IQR) equals Q3 minus Q1, representing the middle 50% of values.

Quartiles help identify outliers, skewness, and data consistency. They are fundamental to box plots, which use Q0 (min), Q1, Q2, Q3, and Q4 (max) to visualize data distributions.

How to Use Quartiles

Calculation Steps

1
Sort your data
Arrange all values in ascending order from smallest to largest.
2
Find percentiles
Q1 is the 25th percentile, Q2 is the 50th (median), Q3 is the 75th percentile.
3
Calculate IQR
Interquartile range equals Q3 minus Q1, measuring the spread of the middle 50%.
4
Identify outliers
Values beyond 1.5 times IQR from Q1 or Q3 are typically considered outliers.

Example: Test Scores

Dataset: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49

Sorted
6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
Quartiles
Q0 (min): 6
Q1 (25%): 15.25
Q2 (50%): 40
Q3 (75%): 43.25
Q4 (max): 49
IQR
IQR = Q3 - Q1 = 43.25 - 15.25 = 28

FAQ About Quartiles

What does Q2 represent?

Q2 is the 50th percentile, also known as the median. Half the data falls below it, half above it.

What is IQR used for?

The IQR (Q3 minus Q1) measures variability in the middle 50% of data and is crucial for identifying outliers in box plots.

How do outliers relate to IQR?

Values below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR are typically considered statistical outliers.

Can I have negative quartiles?

Yes! If your dataset contains negative values, quartiles can be negative. Quartiles reflect the actual data distribution.

What difference between median and quartiles?

The median divides data in half (Q2). Quartiles divide it into four parts (Q0, Q1, Q2, Q3, Q4), showing more detail about distribution.

What minimum sample size?

Technically you need at least 1 value, but quartiles are most meaningful with larger samples. We require at least 4 values.

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