Formula

Five number summary includes five values

1. Minimum value 2. First quartile `Q_1` 3. Median `Q_2` 4. Third quartile `Q_3` 5. Maximum value

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Examples
1. Calculate Box and Whisker Plots from the following data
`10,50,30,20,10,20,70,30`

Solution:
Box and Whisker Plots :
`10,50,30,20,10,20,70,30`

Steps of Five-Number Summary

Step-1: Arrange the numbers in ascending order
`10,10,20,20,30,30,50,70`

Step-2: Find the minimum value
Minimum `=10` (the smallest number)

Step-3: Find the maximum value
Maximum `=70` (the largest number)

Step-4: Find the median
The median is the middle number in a sorted data set and N is the total number of elements
If N is odd then the median is a single middle number, and if N is even then the median is the average of the two middle numbers.

`10,10,20,20,30,30,50,70`

`N=8` is even, so median is the average of the two middle numbers at position 4 and 5

We have `(20+30)/2=25`

`:.` Median `=25`

Step-5: Place parentheses around the numbers above and below the median.
`{10,10,20,20},{30,30,50,70}`

Step-6: Find `Q_1` by finding the median for lower half of data(left of the median)

`10,10,20,20`

`N=4` is even, so median is the average of the two middle numbers at position 2 and 3

We have `(10+20)/2=15`

`:.Q_1=15`

Step-7: Find `Q_3` by finding the median for upper half of data(right of the median)

`30,30,50,70`

`N=4` is even, so median is the average of the two middle numbers at position 2 and 3

We have `(30+50)/2=40`

`:.Q_3=40`

Step-8: Summary found in the above steps.
Minimum `=10`

`Q_1=15`

Median `=25`

`Q_3=40`

Maximum `=70`

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