Question

determine if there are any outliers in the skewed dataset 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25. enter the number of the correct option. option #1: there are no outliers in the dataset. option #2: the value 25 is the only outlier in the dataset. option #3: the values 25 and 19 are the only two outliers in the dataset. option #4: the values 25, 19, and 15 are the only three outliers in the dataset. (1 point) the accurate statement is option #. check answer remaining attempts: 3

Explanation:

Step1: Sort the data

First, sort the dataset \(11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 19, 25\).

Step2: Calculate quartiles

Find the first quartile \(Q_1\). The lower half of the data is \(11, 12, 12, 13, 13, 13\). So, \(Q_1=\frac{12 + 13}{2}=12.5\).
Find the third quartile \(Q_3\). The upper half of the data is \(14, 14, 15, 19, 25\). So, \(Q_3=\frac{14+15}{2} = 14.5\).

Step3: Calculate IQR

Inter - quartile range \(IQR=Q_3 - Q_1=14.5-12.5 = 2\).

Step4: Determine bounds for outliers

Lower bound \(=Q_1-1.5\times IQR=12.5-1.5\times2=9.5\).
Upper bound \(=Q_3 + 1.5\times IQR=14.5+1.5\times2=17.5\).
Values less than \(9.5\) or greater than \(17.5\) are outliers. \(19\) and \(25\) are greater than \(17.5\), and \(15\) is not.

Answer:

Option #3