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Five Number Summary



How does five number summary calculator work?

  • Enter the comma-separated values in the required input field.
  • Press the calculate button.
  • The step-by-step solution will come in a couple of seconds.





5 number summary calculator


Five number summary calculator is an online tool used to calculate the five-number summary of the set of comma-separated values. It also offers the least to the greatest form of the given list of numbers.


What is the 5 number summary?


A set of descriptive statistics that offers information about a data set is said to be the 5 number summary. The 5 sample percentiles that are offered by a five-number summary are:

  1. Minimum value
  2. Lower (First) quartile Q1
  3. Median
  4. Upper (third) quartile Q3
  5. Maximum value

Formulas of a 5 number summary


Here are the formulas for the five terms of the five-number summary.


For minimum and maximum values


Arrange the data set either in ascending or descending order. In the case of ascending order, the first term is the minimum term and the last term is the maximum. While in the case of descending order, the first term is the maximum and the last term is the minimum term.


For the first quartile


Take the lower half of the arranged data set and calculate the median of the first half. The first quartile is 25% of the data set. The formula of the lower quartile is:

lower quartile formula


For Median 


If the total terms of the data set are odd, then the formula of the median is:

medain formula for odd term

If the total terms of the data set are even, then the formula of the median is:

median formula for even terms


For the upper quartile


Take the upper half of the arranged data set and calculate the median of the upper half. The third quartile is 75% of the data set. 

upper quartile formula


How to calculate the five-number summary?


To learn how to calculate the five-number summary, follow the below example.

Example 

Calculate the five-number summary of the given set of data.

23, 7, 18, 5, 12, 13, 25, 8, 19

Solution

Step 1: Frist of all, arrange the data set from least to greatest.

5, 7, 8, 12, 13, 18, 19, 23, 25

Total number of observation = n = 9

Step 2: Now find the maximum and minimum value of the data set.

The first term of the arranged data must be the minimum and the last term must be the maximum.

First term = minimum = 5

Last term = maximum = 25

Step 3: Calculate the first quartile of the data set by using a formula.

First quartile = Q1 = ((n + 1)/4)th term

Put n = 9

First quartile = Q1 = ((9 + 1)/4)th term

                       = Q1 = ((10)/4)th term

                       = Q1 = ((5/2)th term

                       = Q1 = 2.5th term

Hence the first quartile is the 2.5th term of the arranged set of data. It will be the mean of the 2nd and 3rd terms.

First quartile = Q1 = 7 + 8 / 2

                       = Q1 = 15/2 = 7.5

Step 4: Calculate the second quartile (median) of the data set by using the formula.

Median = Q2 = ((n + 1)/2)th term

Put n = 9

Median = Q2 = ((9 + 1)/2)th term

               = Q2 = ((10)/2)th term

               = Q2 = 5th term

Hence the median is the 5th term of the arranged data set.

Median = Q2 = 13

Step 5: Calculate the third quartile of the data set by using a formula.

Third quartile = Q3 = (3(n + 1)/4)th term

Put n = 9

Third quartile = Q3 = (3(9 + 1)/4)th term

                         = Q3 = (3(10)/4)th term

                         = Q3 = (30)/4)th term

                         = Q3 = (15)/2)th term

                         = Q3 = 7.5th term

Hence the third quartile is the 7.5th term of the arranged set of data. It will be the mean of the 7th and 8th terms.

Upper quartile = Q3 = 19 + 23 / 2

Upper quartile = Q3 = 42/2

Upper quartile = Q3 = 21

Step 6: Write all the results of the five-number summary.

Minimum term = 5

First quartile = Q1 = 7.5

Median = Q2 = 13

Third quartile = Q3 = 11

Maximum term = 25