Question

determine any outliers for the data set. select all that apply.
6, 6, 12, 13, 14, 19, 22, 56
a 6
b 14
c 70
d 56

Explanation:

Step1: Find quartiles

First, find the median of the data set. Since there are 8 data points, the median is the average of the 4th and 5th values. The data set is \(6,6,12,13,14,19,22,56\). The median \(Q_2=\frac{13 + 14}{2}=13.5\).
The lower half of the data is \(6,6,12,13\), and its median \(Q_1=\frac{6+12}{2} = 9\).
The upper half of the data is \(14,19,22,56\), and its median \(Q_3=\frac{19+22}{2}=20.5\).

Step2: Calculate IQR

The inter - quartile range \(IQR=Q_3 - Q_1=20.5 - 9 = 11.5\).

Step3: Determine bounds for outliers

The lower bound for non - outliers is \(Q_1-1.5\times IQR=9-1.5\times11.5=9 - 17.25=- 8.25\).
The upper bound for non - outliers is \(Q_3 + 1.5\times IQR=20.5+1.5\times11.5=20.5 + 17.25=37.75\).

Step4: Check for outliers

Values less than \(-8.25\) or greater than \(37.75\) are outliers. In the data set, \(56>37.75\).

Answer:

D. 56