5 Number Summary - Statistics Basics

What is 5 no summary?

5 no summary is an statistical measure to get the idea about the data tendency.

It includes :

1.  Minimum
2.  Q1 (25 percentile)
3.  Median (middle value or 50 percentile)
4.  Q3 (75 percentile)
5.  Maximum

How to calculate or get these values??

Input data :  45, 67, 23, 12, 9, 43, 12, 17, 91

Step1:  Sort the data

9, 12, 12, 17, 23, 43, 45, 67, 91

Step2:  You can easily get the minimum and maximum no

Min : 9

Max : 91

Step 3: Finding the median - Finding the middle value, dont confuse with Mean or Average. 

How to get Median/Middle value - 

a. Sort the data into increasing order

b. Get total no of elements - N

     if N is even -  median =   ( N/2th element + [N/2 + 1]th element) / 2

     if N is odd - median = ceil(N/2)th element

For our case, N = 9, which is odd, so ceil(9/2) = ceil(4.5) = 5th element 

Median = 23

Step 4: Finding our the Q1 and Q3 (called Quantile) is very easy. Divide the element list into 2 list by Median value - 

 (9, 12, 12, 17), 23, (43, 45, 67, 91) 

Now, Find out the Median for 1st list which is Q1 and Median for 2nd list which is Q3

As we can see, list1 and list2 both are having even no of elements so  - 

Median of list1 (Q1) =  ( N/2th element + [N/2 + 1]th element) / 2

                                  =  ( 4/2th element + [4/2 +1]th element) / 2

                                  =  ( 2nd element  + 3rd element ) /2

                                  =  (12 + 12 ) / 2 

                            Q1 = 12

Median of list2 (Q3) = ( 45 + 67 ) / 2

                                  = 112 / 2

                                  = 56 

We got the Q1 (12) and Q3 (56). 

Our 5 no summary is calculated which is -  

min, Q1, median, Q3, max 

9,     12,  23,         56, 91

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