How to Find the Five Number Summary in Statistics

Reviewed by Joseph Meyer

Last Updated: June 9, 2024

The five number summary is an important way of organizing data to show statistical importance through dispersion. This summary consists of the minimum, Quartile 1 (Q1), median (Q2), Quartile 3 (Q3), and the maximum; usually organized in that specific order on a box plot. The lower quartile (Q1) consists of the lower 25% of the data while the upper quartile (Q3) contains 25% of the highest numbers in the data set or 75% of the entire data. This statistical analysis is very useful for larger data because the median identifies the center of the data, the minimum and maximum gives the length of the data and the quartiles allows for further analysis of an assortment. ^{[1]
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Part 1

Part 1 of 6:

Preparing the Data for Calculation

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1
Determine the amount of numbers in your data set. You can do this by counting all of the numbers in the data set.
- Example: In a data set 1,3,4,5,11,12,14,20,11,2 there are 10 numbers in the data set
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2
Organize the data in increasing order. Starting with the smallest number value up to the largest number.
- Organize the data by scanning and writing down the numbers in increasing number.
- While scanning cross out the numbers that were already used to keep track
- Example: In a data set 1,3,4,5,11,12,14,20,11,2 the numbers would be organized as 1,2,3,4,5,11,11,12,14,20
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3
Write down or memorize the equations for both quartiles and the median.
- The 1st Quartie equation ¼ (n+1)
- The median equation ½(n+1)
- The 3rd Quartile ¾(n+1)

Part 2

Part 2 of 6:

Finding the Minimum and Maximum

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1
Find the smallest and the largest numbers of the total data set. In a data set organized in increasing order the minimum is the first number and the maximum in the last number.
- Example: In a data set 1,2,3,4,5,11,11,12,12,14,20 (organized in increasing order) the minimum is 1 (lowest) and maximum is 20 (largest).