8. for the following data, determine if there are any outliers. (use both formulas) 6, 24, 84, 13, 9, 30…

Explanation:

Step1: Arrange data in ascending order

$6,7,9,13,21,24,25,30,33,71,84$

Step2: Calculate the median (Q2)

Since $n = 11$ (odd - numbered data set), $Q2$ is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{11+ 1}{2}=6$ - th value. So $Q2 = 24$.

Step3: Calculate the lower half and its median (Q1)

The lower - half data is $6,7,9,13,21$. Since $n = 5$ (odd - numbered), $Q1$ is the $\left(\frac{5 + 1}{2}\right)$-th value. So $Q1=9$.

Step4: Calculate the upper half and its median (Q3)

The upper - half data is $25,30,33,71,84$. Since $n = 5$ (odd - numbered), $Q3$ is the $\left(\frac{5+ 1}{2}\right)$-th value. So $Q3 = 33$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=33 - 9 = 24$.

Step6: Calculate the lower fence

Lower fence $=Q1-1.5\times IQR=9-1.5\times24=9 - 36=-27$.

Step7: Calculate the upper fence

Upper fence $=Q3 + 1.5\times IQR=33+1.5\times24=33 + 36 = 69$.

Step8: Identify outliers

Values less than the lower fence or greater than the upper fence are outliers. The values $71$ and $84$ are greater than $69$. So $71$ and $84$ are outliers.

Answer:

The outliers are 71 and 84.