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 grouped data

X	Frequency
0	1
1	5
2	10
3	6
4	3

Solution:
Box and Whisker Plots :

`x`	Frequency `f`	`cf`
0	1	1
1	5	6
2	10	16
3	6	22
4	3	25
---	---	---
	n = 25	--

Minimum value `=0`

Maximum value `=4`

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First quartile `Q_1` :

Here, `n = 25`

`Q_1 = ((n+1)/4)^(th)` value of the observation

`=(26/4)^(th)` value of the observation

`=(6.5)^(th)` value of the observation

`=2`

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Median `Q_2` :

`Q_2 = ((2(n+1))/4)^(th)` value of the observation

`=((2*26)/4)^(th)` value of the observation

`=(13)^(th)` value of the observation

`=2`

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Third quartile `Q_3` :

`Q_3 = ((3(n+1))/4)^(th)` value of the observation

`=((3*26)/4)^(th)` value of the observation

`=(19.5)^(th)` value of the observation

`=3`

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Thus Five number summary is
1. Minimum value `=0`

2. First quartile `Q_1=2`

3. Median `Q_2=2`

4. Third quartile `Q_3=3`

5. Maximum value `=4`

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