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Five Number Summary Calculator

Find the minimum, Q1, median, Q3, and maximum values of any data set. Get the interquartile range, range, sorted data, and detailed statistical calculations instantly.

Calculate Five Number Summary

Enter your numerical data to calculate all five summary values.

Separate values with commas, spaces, or line breaks. Decimal and negative numbers are supported.
Try Example Data
Five Number Summary
Summary Calculated Successfully
Minimum 0
Q1 0
Median / Q2 0
Q3 0
Maximum 0
Interquartile Range 0
Total Range 0

What Is a Five Number Summary?

A five number summary is a simple statistical description of a numerical data set. It uses five important values to show the center, spread, and overall range of the data.

The five values are the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Together, they provide a useful overview of how the data is distributed.

Five Number Summary = Minimum, Q1, Median, Q3, Maximum

How Does the Five Number Summary Calculator Work?

The calculator first arranges your data values from smallest to largest. It then calculates the three quartiles using the linear interpolation method and identifies the minimum and maximum values.

  1. Enter all numerical values from your data set.
  2. The calculator automatically sorts the values in ascending order.
  3. The smallest value becomes the minimum.
  4. Q1 is calculated at the 25th percentile.
  5. Q2 is calculated at the 50th percentile and represents the median.
  6. Q3 is calculated at the 75th percentile.
  7. The largest value becomes the maximum.
  8. The calculator also calculates IQR and the total range.

The Five Values Explained

1. Minimum

The minimum is the smallest value in the data set. It represents the lower endpoint of the observed data.

2. First Quartile — Q1

Q1 is the 25th percentile. Approximately 25% of the observations are at or below this value.

3. Median — Q2

The median is the middle value of a sorted data set and is also called the second quartile, Q2, or 50th percentile.

4. Third Quartile — Q3

Q3 is the 75th percentile. Approximately 75% of the observations are at or below this value.

5. Maximum

The maximum is the largest value in the data set and represents the upper endpoint of the observed data.

Five Number Summary Formulas

The quartile calculations in this tool use the linear interpolation position formula:

Position = (P ÷ 100) × (n − 1)

First Quartile

Q1 = P25

Median

Q2 = P50 = Median

Third Quartile

Q3 = P75

Interquartile Range

IQR = Q3 − Q1

Total Range

Range = Maximum − Minimum

Five Number Summary Example

Consider the following data set:

10, 20, 30, 40, 50, 60, 70

The five number summary using the linear interpolation method is:

Minimum = 10
Q1 = 25
Median = 40
Q3 = 55
Maximum = 70

The interquartile range is:

IQR = 55 − 25 = 30

The total range is:

Range = 70 − 10 = 60

Why Is a Five Number Summary Useful?

A five number summary gives a compact picture of a data distribution without requiring every observation to be examined individually.

Understand Data Spread

The minimum and maximum show the overall boundaries, while Q1 and Q3 show the boundaries of the middle portion of the data.

Identify Potential Outliers

Q1, Q3, and IQR can be used with the 1.5 × IQR rule to identify observations that may be unusually low or high.

Create Box Plots

The five number summary is the foundation of a box-and-whisker plot. The five values help describe the shape and spread of a distribution visually.

Frequently Asked Questions

The five values are the minimum, Q1, median (Q2), Q3, and maximum.
Q1 is the first quartile and represents the 25th percentile of the data set.
Q2 is the second quartile and is equal to the median or 50th percentile.
Q3 is the third quartile and represents the 75th percentile of the data.
IQR stands for interquartile range. It measures the spread of the middle 50% of the data and is calculated as Q3 − Q1.
Yes. You can enter values in any order. The calculator automatically sorts them from smallest to largest before performing the calculations.
Yes. The calculator supports positive numbers, negative numbers, and decimal values.
Q1, Q2, and Q3 are calculated using a linear interpolation percentile method based on the position (P ÷ 100) × (n − 1).