3. Example-3
3. Calculate Five number summary from the following data
`3,13,11,15,5,4,2`
Solution:
Five number summary :
`3,13,11,15,5,4,2`
Steps of Five-Number Summary
Step-1: Arrange the numbers in ascending order
`2,3,4,5,11,13,15`
Step-2: Find the minimum value
Minimum `=2` (the smallest number)
Step-3: Find the maximum value
Maximum `=15` (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.
`2,3,4,5,11,13,15`
`N=7` is odd, so median is the middle number at position 4
We have `5`
`:.` Median `=5`
Step-5: Place parentheses around the numbers above and below the median.
`{2,3,4},5,{11,13,15}`
Step-6: Find `Q_1` by finding the median for lower half of data(left of the median)
`2,3,4`
`N=3` is odd, so median is the middle number at position 2
We have `3`
`:.Q_1=3`
Step-7: Find `Q_3` by finding the median for upper half of data(right of the median)
`11,13,15`
`N=3` is odd, so median is the middle number at position 2
We have `13`
`:.Q_3=13`
Step-8: Summary found in the above steps.
Minimum `=2`
`Q_1=3`
Median `=5`
`Q_3=13`
Maximum `=15`
This material is intended as a summary. Use your textbook for detail explanation.
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