Calculate Five number summary from the following grouped data

X	Frequency
10	3
11	12
12	18
13	12
14	3

Solution:
Five number summary :

`x`	Frequency `f`	`cf`
10	3	3
11	12	15
12	18	33
13	12	45
14	3	48
---	---	---
	n = 48	--

Minimum value `=10`

Maximum value `=14`

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First quartile `Q_1` :

Here, `n = 48`

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

`=(49/4)^(th)` value of the observation

`=(12.25)^(th)` value of the observation

`=11`

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Median `Q_2` :

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

`=((2*49)/4)^(th)` value of the observation

`=(24.5)^(th)` value of the observation

`=12`

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Third quartile `Q_3` :

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

`=((3*49)/4)^(th)` value of the observation

`=(36.75)^(th)` value of the observation

`=13`

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Thus Five number summary is
1. Minimum value `=10`

2. First quartile `Q_1=11`

3. Median `Q_2=12`

4. Third quartile `Q_3=13`

5. Maximum value `=14`

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