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Viva Calculator

5 Number Summary Calculator

Calculate the five-number summary of your dataset including quartiles

Calculate Summary

Separate values with commas, spaces, or semicolons

Method and source check

Last checked:

Source and implementation check; this is not professional review or advice.

Method

The calculator validates at least two finite numbers, sorts them, and reports the minimum, 25th percentile, median, 75th percentile, and maximum. Percentiles use linear interpolation with zero-based position h = (n − 1)p; range and IQR are derived from those values.

Q(p) = x⌊h⌋ + (h − ⌊h⌋)(x⌊h⌋+1 − x⌊h⌋), h = (n − 1)p

IQR = Q3 − Q1

range = maximum − minimum

Variables and units

x
the data sorted in ascending order
p
0.25, 0.50, or 0.75
n
number of data values

Worked example

For 1, 2, 3, 4: minimum = 1, Q1 = 1.75, median = 2.5, Q3 = 3.25, maximum = 4, IQR = 1.5, and range = 3.

Limitations

  • Quartile conventions differ among books and software. This calculator uses the stated linear-interpolation convention, so Q1 and Q3 can differ from tools that use lower- and upper-half medians.

Sources

Table of Contents

How to Use

  1. Enter your data values separated by commas, spaces, or semicolons
  2. Click calculate to compute the five-number summary
  3. Review the minimum, Q1, median, Q3, maximum, range, and IQR

What is the Five-Number Summary?

The five-number summary is a descriptive statistic that provides information about a dataset using five key values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

These five numbers divide the dataset into four equal parts, with 25% of the data falling between each consecutive pair of values. This summary is the basis for creating box plots (box-and-whisker plots).

Components of the Five-Number Summary

  • Minimum: The smallest value in the dataset
  • Q1 (First Quartile): The 25th percentile, estimated here by linear interpolation
  • Median (Q2): The middle value that divides the dataset in half (50th percentile)
  • Q3 (Third Quartile): The 75th percentile, estimated here by linear interpolation
  • Maximum: The largest value in the dataset

Additional Measures

In addition to the five-number summary, this calculator provides:

  • Range: The difference between the maximum and minimum values, showing the spread of the entire dataset
  • IQR (Interquartile Range): The difference between Q3 and Q1, representing the middle 50% of the data and used to identify outliers

Applications

  • Creating box plots for visual data representation
  • Comparing distributions between different datasets
  • Identifying outliers using the IQR method
  • Understanding data spread and central tendency
  • Quality control in manufacturing
  • Academic research and data analysis

Frequently Asked Questions

What is the difference between median and Q2?
The median and Q2 (second quartile) are the same value. Both represent the middle point of the dataset where 50% of values fall below and 50% fall above.
How is the IQR used to detect outliers?
Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are typically considered outliers. This is a common method in box plot analysis.
Can I use this calculator for small datasets?
Yes, you need at least 2 values, though the five-number summary is most informative with larger datasets (typically 10 or more values).
What if my dataset has an even number of values?
The calculator uses interpolation to find quartiles when needed. For even datasets, the median is the average of the two middle values.

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