1. Formula & Example-1
Formula
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Five number summary includes five values
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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 Five number summary from the following data
`10,50,30,20,10,20,70,30`
Solution:
Five number summary :
`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`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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