How to calculate the 5 Number Summary?
Last Updated :
20 Jan, 2022
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)/2th 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.
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
Here we need to find median value by a formula (n + 1)/2th term where n is the total count of numbers.
Here n = 7
So median = (7 + 1)/2 = 8/2 = 4th term
4th 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
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
= 2nd term
2nd term is 8 So, Quartile-1 = 8
In the same way find the quartile-3 using the formula (3(n + 1)/4)th term.
Quartile 3 = (3(7 + 1)/4)th term
= (3(8)/4)th term
= (24/4)th term
= 6th term
6th 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:
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
= 4.5th term
4.5th term is the average value of 4th and 5th 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
= 2.25th term
2.25th term is the average value of 2nd and 3rd 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
= 6.75th term
6.75th term is the average value of 6th and 7th term values
Quartile-3 = (12 + 14)/2
= 26/2 = 13
Quartile-3 = 13
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