How to calculate the 5 Number Summary? - GeeksforGeeks (2024)

The concept of a 5 number summary is a way to describe a distribution using 5 numbers. This includes minimum number, quartile-1, median/quartile-2, quartile-3, and maximum number. This concept of 5 number summary comes under the concept of Statistics which deals with the collection of data, analyzing it, interpreting, and presenting the data in an organized manner.

5 Number Summary

As told in the above paragraph, It gives a rough idea how the given dataset looks like by representing minimum value, maximum value, median, quartile values, etc. To understand better the 5 number summary concept look at the below pictorial representation of 5 number summary

Calculating 5 number summary

In order to find the 5 number summary, we need the data to be sorted. If not sort it first in ascending order and then find it.

• Minimum Value: It is the smallest number in the given data, and the first number when it is sorted in ascending order.
• Maximum Value: It is the largest number in the given data, and the last number when it is sorted in ascending order.

Median: Middle value between the minimum and maximum value. Below is the formula to find median,

Median = (n + 1)/2^th term

• Quartile 1: Middle/center value between the minimum and median value. We can simply identify the middle value between median and minimum value for a small dataset. If it is a big dataset with so many numbers then better to use a formula,

Quartile 1 = ((n + 1)/4)^th term

• Quartile 3: Middle/center value between median and maximum value.

Quartile 3 = (3(n + 1)/4)^th term

To get more grip on this let’s look at the few examples,

Sample Questions

Question 1: What is the minimum value in the given data 10, 20, 5, 15, 25, 30, 8.

Solution:

• Step-1 Sort the given data in ascending order.

5, 8, 10, 15, 20, 25, 30

• Step-2 Find minimum number

Here the first number is the minimum number as it is sorted in ascending order.

See Also

Five-Number Summary in Statistics: A Detailed GuideHow to Find the Five Number Summary in Statistics (with Pictures)How to Find a Five Number Summary – mathsathome.com5 Number Summary Calculator

Minimum value = 5

Question 2: What is the maximum value in the given data 10, 20, 5, 15, 25, 30, 8.

Solution:

• Step-1 Sort the given data in ascending order.

5, 8, 10, 15, 20, 25, 30

• Step-2 Find maximum number

Here the last number is the maximum number as it is sorted in ascending order.

Maximum value = 30

Question 3: What is the median value in the given data 10, 20, 5, 15, 25, 30, 8

Solution:

• Step-1 Sort the given data in ascending order.

5, 8, 10, 15, 20, 25, 30

• Step-2 Find median

Here we need to find median value by a formula (n + 1)/2^th term where n is the total count of numbers.

Here n = 7

So median = (7 + 1)/2 = 8/2 = 4^th term

4^th term is median which is 15.

Question 4: Find the 5 number summary for the given data 10, 20, 5, 15, 25, 30, 8

Solution:

• Step-1 Sort the given data in ascending order.

5, 8, 10, 15, 20, 25, 30

• Step-2

As the given data is same as the above examples we can get minimum value, median and maximum from there.

So, Minimum = 5

Maximum = 30

Median = 15

Now find 1st and 3rd quartile either by using formula or by picking center value. Both gives same result.

For Quartile-1 Formula is ((n + 1)/4)^th term where n is the count of numbers in the dataset.

n = 7 because there are 7 numbers in the data.

Quartile-1 = ((7 + 1)4)^th term

= (8/4)^th term

= 2^nd term

2^nd term is 8 So, Quartile-1 = 8

In the same way find the quartile-3 using the formula (3(n + 1)/4)^th term.

See Also

Exploring the 5 Number Summary: Understanding the Basics with Examples and Formulas

Quartile 3 = (3(7 + 1)/4)^th term

= (3(8)/4)^th term

= (24/4)^th term

= 6^th term

6^th term is 25 so Quartile-3 = 25

Question 5: Find out the 5 number summary for the data 1, 10, 5, 15, 2, 12, 4, 14.

Solution:

• Step-1 Sort data

1, 2, 4, 5, 10, 12, 14, 15

• Step-2 Find min, max, median, quartile values.

Minimum value = 1

Maximum value = 15

Median = ((n + 1)/2)^th term

Here n = 8

= ((8 + 1)/2)^th term

= (9/2)^th term

= 4.5^th term

4.5^th term is the average value of 4^th and 5^th term values

Median = (5 + 10)/2

=15/2 = 7.5

Median = 7.5

Quartile-1 = ((n + 1)/4)^th term

= ((8 + 1)/4)^th term

= (9/4)^th term

= 2.25^th term

2.25^th term is the average value of 2^nd and 3^rd term values

Quartile-1 = (2 + 4)/2

= 6/2 = 3

Quartile-1 = 3

Quartile-3 = (3(n + 1)/4)^th term

= (3(8 + 1)/4)^th term

= (3(9)/4)^th term

= (27/4)^th term

= 6.75^th term

6.75^th term is the average value of 6^th and 7t^h term values

Quartile-3 = (12 + 14)/2

= 26/2 = 13

Quartile-3 = 13