Answer:
An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. ... Examination of the data for unusual observations that are far removed from the mass of data. These points are often referred to as outliers. Which explains whether or not 12 is an outlier? Twelve is not an outlier because it is less than the sum of 7 and 6.
Step-by-step explanation:
In the given dataset, twelve is not an outlier because it is less than the sum of 7 and 6.
The outlier of a dataset is the date that are distant from other values of the dataset.
Given that:
[tex]S = \{ 2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 12\}[/tex] --- the dataset
[tex]N = 11[/tex] -- number of observations
[tex]IQR = 4[/tex]
The position of the lower quartile of the above set is:
[tex]Q_1 = \frac{1}{4} \times (N + 1)th[/tex]
[tex]Q_1 = \frac{1}{4} \times (11 + 1)th[/tex]
[tex]Q_1 = \frac{1}{4} \times (12)th[/tex]
[tex]Q_1 = 3rd[/tex]
The 3rd element is 3. So:
[tex]Q_1 = 3[/tex]
Similarly, the position of the upper quartile of the above set is:
[tex]Q_3 = \frac{3}{4} \times (N + 1)th[/tex]
[tex]Q_3 = \frac{3}{4} \times (11 + 1)th[/tex]
[tex]Q_3 = \frac{3}{4} \times (12)th[/tex]
[tex]Q_3 = 9th[/tex]
The 9th element is 7. So:
[tex]Q_3 = 7[/tex]
The lower outlier (L) is
[tex]L = Q_1 - (1.5 \times IQR)[/tex]
[tex]L = 3 - (1.5 \times 4)[/tex]
[tex]L = 3 - 6[/tex]
[tex]L = - 3[/tex]
The upper outlier (U) is:
[tex]U = Q_1 + (1.5 \times IQR)[/tex]
[tex]U = 7 + (1.5 \times 4)[/tex]
[tex]U = 7 + 6[/tex]
[tex]U= 13[/tex]
Values from the lower to the upper outliers are not outliers.
In other words
[tex]-3, -2, -1, 0, 1, 2,......,11,12,13[/tex] are not outliers
12 is not an outlier because it is less than 13
13 is gotten from 7 + 6; as in: [tex]U = 7 + 6[/tex]
Hence, (d) is correct
Read more about outliers at:
https://brainly.com/question/12153650
