Given:
The five number summary of two data sets are given as:
a) 0, 4, 12, 14, 20
b) 2, 8, 14, 18, 20
To find:
The range for the outliers.
Solution:
We know that,
An observation is considered an outlier if it is below ![Q_1-1.5(IQR)](https://tex.z-dn.net/?f=Q_1-1.5%28IQR%29)
An observation is considered an outlier if it is above ![Q_3+1.5(IQR)](https://tex.z-dn.net/?f=Q_3%2B1.5%28IQR%29)
Where, IQR is the interquartile range and
.
The five number summary of two data sets are given as:
0, 4, 12, 14, 20
Here,
and
.
Now,
![IQR=14-4](https://tex.z-dn.net/?f=IQR%3D14-4)
![IQR=10](https://tex.z-dn.net/?f=IQR%3D10)
The range for the outliers is:
![[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)]](https://tex.z-dn.net/?f=%5BQ_1-1.5%28IQR%29%2CQ_3%2B1.5%28IQR%29%5D%3D%5B4-1.5%2810%29%2C14%2B1.5%2810%29%5D)
![[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15]](https://tex.z-dn.net/?f=%5BQ_1-1.5%28IQR%29%2CQ_3%2B1.5%28IQR%29%5D%3D%5B4-15%2C14%2B15%5D)
![[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29]](https://tex.z-dn.net/?f=%5BQ_1-1.5%28IQR%29%2CQ_3%2B1.5%28IQR%29%5D%3D%5B-11%2C29%5D)
An observation is considered an outlier if it is below -11.
An observation is considered an outlier if it is above 29.
The five number summary of two data sets are given as:
2, 8, 14, 18, 20
Here,
and
.
Now,
![IQR=18-8](https://tex.z-dn.net/?f=IQR%3D18-8)
![IQR=10](https://tex.z-dn.net/?f=IQR%3D10)
The range for the outliers is:
![[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)]](https://tex.z-dn.net/?f=%5BQ_1-1.5%28IQR%29%2CQ_3%2B1.5%28IQR%29%5D%3D%5B8-1.5%2810%29%2C18%2B1.5%2810%29%5D)
![[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15]](https://tex.z-dn.net/?f=%5BQ_1-1.5%28IQR%29%2CQ_3%2B1.5%28IQR%29%5D%3D%5B8-15%2C18%2B15%5D)
![[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33]](https://tex.z-dn.net/?f=%5BQ_1-1.5%28IQR%29%2CQ_3%2B1.5%28IQR%29%5D%3D%5B-7%2C33%5D)
An observation is considered an outlier if it is below -7.
An observation is considered an outlier if it is above 33.