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`
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`
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`
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`
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`
This material is intended as a summary. Use your textbook for detail explanation.
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