2. Example-2
Calculate Five number summary from the following data
`85,96,76,108,85,80,100,85,70,95`
Solution:
Five number summary :
`85,96,76,108,85,80,100,85,70,95`
Steps of Five-Number Summary
Step-1: Arrange the numbers in ascending order
`70,76,80,85,85,85,95,96,100,108`
Step-2: Find the minimum value
Minimum `=70` (the smallest number)
Step-3: Find the maximum value
Maximum `=108` (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.
`70,76,80,85,85,85,95,96,100,108`
`N=10` is even, so median is the average of the two middle numbers at position 5 and 6
We have `(85+85)/2=85`
`:.` Median `=85`
Step-5: Place parentheses around the numbers above and below the median.
`{70,76,80,85,85},{85,95,96,100,108}`
Step-6: Find `Q_1` by finding the median for lower half of data(left of the median)
`70,76,80,85,85`
`N=5` is odd, so median is the middle number at position 3
We have `80`
`:.Q_1=80`
Step-7: Find `Q_3` by finding the median for upper half of data(right of the median)
`85,95,96,100,108`
`N=5` is odd, so median is the middle number at position 3
We have `96`
`:.Q_3=96`
Step-8: Summary found in the above steps.
Minimum `=70`
`Q_1=80`
Median `=85`
`Q_3=96`
Maximum `=108`
This material is intended as a summary. Use your textbook for detail explanation.
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