Question

potential outliers
determine if there are any potential outliers to the following data.
ex: 50, 53, 55, 59, 62, 68, 71, 75, 78, 80, 82, 130

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending order: 50, 53, 55, 59, 62, 68, 71, 75, 78, 80, 82, 130

Step2: Calculate the first quartile ($Q_1$)

The position of $Q_1$ is $\frac{n + 1}{4}=\frac{12+ 1}{4}=3.25$. So $Q_1 = 55+(59 - 55)\times0.25=56$.

Step3: Calculate the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(12 + 1)}{4}=9.75$. So $Q_3=78+(80 - 78)\times0.75 = 79.5$.

Step4: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=79.5 - 56 = 23.5$.

Step5: Calculate the lower and upper bounds for non - outliers

Lower bound: $Q_1-1.5\times IQR=56-1.5\times23.5=56 - 35.25 = 20.75$.
Upper bound: $Q_3 + 1.5\times IQR=79.5+1.5\times23.5=79.5 + 35.25=114.75$.

Step6: Identify outliers

Any value less than the lower bound or greater than the upper bound is an outlier. The value 130 is greater than 114.75.

Answer:

The potential outlier is 130.