Question

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

Explanation:

Step1: Find quartiles

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

Step2: Calculate IQR

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

Step3: Determine fences

The lower fence is $Q_1-1.5\times IQR=9 - 1.5\times11.5=9 - 17.25=- 8.25$.
The upper fence is $Q_3 + 1.5\times IQR=20.5+1.5\times11.5=20.5 + 17.25=37.75$.

Step4: Check for outliers

Any number less than the lower fence or greater than the upper fence is an outlier.
$56>37.75$, so 56 is an outlier.
70 is not in the original data set. 6 and 14 are within the fences ($-8.25<6<37.75$ and $-8.25<14<37.75$).

Answer:

B. 56