Outliers are data that are relatively far from other data elements.
The dataset has an outlier and the outlier is 120
The dataset is given as:
- 91 83 84 79 91 93 95 97 97 120 101 105 98
Sort the dataset in ascending order
- 79 83 84 91 91 93 95 97 97 98 101 105 120
<h3>The lower quartile (Q1)</h3>
The Q1 is then calculated as:
![Q1 = \frac{N +1}{4}th](https://tex.z-dn.net/?f=Q1%20%3D%20%5Cfrac%7BN%20%2B1%7D%7B4%7Dth)
So, we have:
![Q1 = \frac{13 +1}{4}th](https://tex.z-dn.net/?f=Q1%20%3D%20%5Cfrac%7B13%20%2B1%7D%7B4%7Dth)
![Q1 = \frac{14}{4}th](https://tex.z-dn.net/?f=Q1%20%3D%20%5Cfrac%7B14%7D%7B4%7Dth)
![Q1 = 3.5th](https://tex.z-dn.net/?f=Q1%20%3D%203.5th)
This is the average of the 3rd and the 4th element
![Q1 = \frac{1}{2} \times (84 + 91)](https://tex.z-dn.net/?f=Q1%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%2884%20%2B%2091%29)
![Q1 = 87.5](https://tex.z-dn.net/?f=Q1%20%3D%2087.5)
<h3>The upper quartile (Q3)</h3>
The Q3 is then calculated as:
![Q3 = 3 \times \frac{N +1}{4}th](https://tex.z-dn.net/?f=Q3%20%3D%20%203%20%5Ctimes%20%5Cfrac%7BN%20%2B1%7D%7B4%7Dth)
So, we have:
![Q3 = 3 \times \frac{13 +1}{4}th](https://tex.z-dn.net/?f=Q3%20%3D%20%203%20%5Ctimes%20%5Cfrac%7B13%20%2B1%7D%7B4%7Dth)
![Q3 = 3 \times 3.5th](https://tex.z-dn.net/?f=Q3%20%3D%20%203%20%5Ctimes%203.5th)
![Q3 = 10.5th](https://tex.z-dn.net/?f=Q3%20%3D%20%2010.5th)
This is the average of the 10th and the 11th element.
![Q_3 =\frac12 \times (98 + 101)](https://tex.z-dn.net/?f=Q_3%20%3D%5Cfrac12%20%5Ctimes%20%2898%20%2B%20101%29)
![Q_3 =99.5](https://tex.z-dn.net/?f=Q_3%20%3D99.5)
<h3>The interquartile range (IQR)</h3>
The IQR is then calculated as:
![IQR = Q_3 -Q_1](https://tex.z-dn.net/?f=IQR%20%3D%20Q_3%20-Q_1)
![IQR = 99.5 - 87.5](https://tex.z-dn.net/?f=IQR%20%3D%2099.5%20-%2087.5)
![IQR = 12](https://tex.z-dn.net/?f=IQR%20%3D%2012)
Also, we have:
![IQR(1.5) = 12 \times 1.5](https://tex.z-dn.net/?f=IQR%281.5%29%20%3D%2012%20%5Ctimes%201.5)
![IQR(1.5) = 18](https://tex.z-dn.net/?f=IQR%281.5%29%20%3D%2018)
<h3>The outlier range</h3>
The lower and the upper outlier range are calculated as follows:
![Lower = Q_1 - IQR(1.5)](https://tex.z-dn.net/?f=Lower%20%3D%20Q_1%20-%20IQR%281.5%29)
![Lower = 87.5- 18](https://tex.z-dn.net/?f=Lower%20%3D%2087.5-%2018)
![Lower = 69.5](https://tex.z-dn.net/?f=Lower%20%3D%2069.5)
![Upper = Q_3 + IQR(1.5)](https://tex.z-dn.net/?f=Upper%20%3D%20Q_3%20%2B%20IQR%281.5%29)
![Upper = 99.5 + 18](https://tex.z-dn.net/?f=Upper%20%3D%2099.5%20%2B%2018)
![Upper = 117.5](https://tex.z-dn.net/?f=Upper%20%3D%20117.5)
120 is greater than 117.5.
Hence, the dataset has an outlier and the outlier is 120
Read more about outliers at:
brainly.com/question/9933184