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:
Sort the dataset in ascending order
The Q1 is then calculated as:
[tex]Q1 = \frac{N +1}{4}th[/tex]
So, we have:
[tex]Q1 = \frac{13 +1}{4}th[/tex]
[tex]Q1 = \frac{14}{4}th[/tex]
[tex]Q1 = 3.5th[/tex]
This is the average of the 3rd and the 4th element
[tex]Q1 = \frac{1}{2} \times (84 + 91)[/tex]
[tex]Q1 = 87.5[/tex]
The Q3 is then calculated as:
[tex]Q3 = 3 \times \frac{N +1}{4}th[/tex]
So, we have:
[tex]Q3 = 3 \times \frac{13 +1}{4}th[/tex]
[tex]Q3 = 3 \times 3.5th[/tex]
[tex]Q3 = 10.5th[/tex]
This is the average of the 10th and the 11th element.
[tex]Q_3 =\frac12 \times (98 + 101)[/tex]
[tex]Q_3 =99.5[/tex]
The IQR is then calculated as:
[tex]IQR = Q_3 -Q_1[/tex]
[tex]IQR = 99.5 - 87.5[/tex]
[tex]IQR = 12[/tex]
Also, we have:
[tex]IQR(1.5) = 12 \times 1.5[/tex]
[tex]IQR(1.5) = 18[/tex]
The lower and the upper outlier range are calculated as follows:
[tex]Lower = Q_1 - IQR(1.5)[/tex]
[tex]Lower = 87.5- 18[/tex]
[tex]Lower = 69.5[/tex]
[tex]Upper = Q_3 + IQR(1.5)[/tex]
[tex]Upper = 99.5 + 18[/tex]
[tex]Upper = 117.5[/tex]
120 is greater than 117.5.
Hence, the dataset has an outlier and the outlier is 120
Read more about outliers at:
https://brainly.com/question/9933184
