TFT

Five Number Summary Calculator – Min Q1 Median Q3 Max

Find the five-number summary of any dataset with our free online calculator. Instantly compute the minimum, Q1, median, Q3, and maximum for complete data analysis.

Enter at least 4 numbers for meaningful quartile calculations.

Examples:

Understanding the Five-Number Summary

The five-number summary gives you a quick snapshot of your data's distribution. It consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Together, these five numbers tell you where your data is centered, how spread out it is, and whether it's symmetric or skewed.

The median splits your data in half. Q1 marks the 25th percentile – a quarter of your data falls below this value. Q3 marks the 75th percentile. The interquartile range (IQR = Q3 - Q1) captures the middle 50% of your data, making it a robust measure of spread that isn't thrown off by outliers.

How to Calculate the Five-Number Summary

  1. 1

    Sort your data

    Arrange all values from smallest to largest. This is essential for finding quartiles.

  2. 2

    Find the minimum and maximum

    The smallest value is your minimum. The largest is your maximum.

  3. 3

    Find the median

    For odd n, it's the middle value. For even n, average the two middle values.

  4. 4

    Find Q1 and Q3

    Q1 is the median of the lower half (excluding the overall median if n is odd). Q3 is the median of the upper half.

  5. 5

    Calculate IQR

    Subtract Q1 from Q3. This tells you the spread of the middle 50% of your data.

Worked Examples

Example 1: Test Scores

Data: 12, 5, 8, 20, 15, 10, 25, 18, 30, 7
Sorted: 5, 7, 8, 10, 12, 15, 18, 20, 25, 30
n = 10 (even)
Min = 5, Max = 30
Median = (12 + 15) / 2 = 13.5
Lower half: 5, 7, 8, 10, 12 → Q1 = 8
Upper half: 15, 18, 20, 25, 30 → Q3 = 20
IQR = 20 - 8 = 12
Five-number summary: 5, 8, 13.5, 20, 30

Example 2: Small Dataset

Data: 3, 7, 8, 12, 15, 18, 22
n = 7 (odd)
Min = 3, Max = 22
Median = 12 (middle value, position 4)
Lower half: 3, 7, 8 → Q1 = 7
Upper half: 15, 18, 22 → Q3 = 18
IQR = 18 - 7 = 11
Five-number summary: 3, 7, 12, 18, 22

Example 3: Identifying Outliers

Using the IQR rule:
Lower fence = Q1 - 1.5 × IQR
Upper fence = Q3 + 1.5 × IQR
Values outside these fences are outliers
From Example 1: IQR = 12
Lower fence = 8 - 1.5(12) = -10
Upper fence = 20 + 1.5(12) = 38
No outliers in this dataset (all values between -10 and 38)

Quick Fact

The five-number summary is the foundation of the box plot (box-and-whisker plot), invented by statistician John Tukey in 1969. Tukey was a pioneer of exploratory data analysis and believed in letting the data "speak for itself" through visual displays.

Frequently Asked Questions

Why use the five-number summary instead of mean and standard deviation?

The five-number summary works better for skewed distributions and datasets with outliers. The median and IQR are resistant to extreme values, while the mean and standard deviation can be heavily influenced by them.

How do I handle even vs odd sample sizes?

For the median: even n means averaging the two middle values; odd n means taking the middle value. For quartiles: exclude the median from both halves when n is odd. When n is even, split the data cleanly in half.

What does the IQR tell me?

The IQR shows how spread out the middle 50% of your data is. A small IQR means values cluster tightly around the median. A large IQR indicates more variability. It's also used to identify outliers.

Can the five-number summary detect skewness?

Yes. Compare the distances: if (Q3 - Median) is much larger than (Median - Q1), the data is right-skewed. If the opposite, it's left-skewed. Similar distances suggest symmetry.

What's the minimum sample size needed?

Technically you need at least 4 values to calculate all five numbers meaningfully. However, the summary becomes more informative with larger samples. Aim for at least 10-15 values for reliable quartiles.

How do I use this for box plots?

The five-number summary directly creates a box plot. The box spans from Q1 to Q3 with a line at the median. Whiskers extend to the minimum and maximum (or to the fences if showing outliers).

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