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`

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