Formula
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Five number summary includes five values
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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
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`
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`
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`
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`
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`
This material is intended as a summary. Use your textbook for detail explanation.
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