Question

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

Explanation:

Step1: Find the median

The data set is \(6,6,12,13,14,19,22,56\). There are \(n = 8\) data points. The median \(Q_{2}\) is the average of the \(4^{th}\) and \(5^{th}\) values.
\(Q_{2}=\frac{13 + 14}{2}=13.5\)

Step2: Find \(Q_{1}\) and \(Q_{3}\)

The lower half of the data is \(6,6,12,13\). The median of the lower half \(Q_{1}\) is the average of the \(2^{nd}\) and \(3^{rd}\) values. \(Q_{1}=\frac{6+12}{2} = 9\)
The upper half of the data is \(14,19,22,56\). The median of the upper half \(Q_{3}\) is the average of the \(2^{nd}\) and \(3^{rd}\) values. \(Q_{3}=\frac{19 + 22}{2}=20.5\)

Step3: Calculate the inter - quartile range (IQR)

\(IQR=Q_{3}-Q_{1}=20.5 - 9=11.5\)

Step4: Determine the outlier boundaries

The lower boundary is \(Q_{1}-1.5\times IQR=9-1.5\times11.5=9 - 17.25=- 8.25\)
The upper boundary is \(Q_{3}+1.5\times IQR=20.5+1.5\times11.5=20.5 + 17.25=37.75\)

Answer:

B. 56