the last 11 calls to a customer support line had the following lengths (in minutes). 15, 52, 52, 53, 54, 55…

the last 11 calls to a customer support line had the following lengths (in minutes). 15, 52, 52, 53, 54, 55, 56, 61, 62, 64, 65. identify all values that are outliers. if there is more than one outlier, separate them with commas. if there are no outliers, click on \none\.

the last 11 calls to a customer support line had the following lengths (in minutes). 15, 52, 52, 53, 54, 55, 56, 61, 62, 64, 65. identify all values that are outliers. if there is more than one outlier, separate them with commas. if there are no outliers, click on \none\.

Answer

Explanation:

Step1: Arrange data in order

$15,52,52,53,54,55,56,61,62,64,65$

Step2: Find Q1 and Q3

There are $n = 11$ data - points. The position of $Q1$ is $\frac{n + 1}{4}=\frac{11+1}{4}=3$. So $Q1 = 52$. The position of $Q3$ is $\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9$. So $Q3 = 62$.

Step3: Calculate the IQR

$IQR=Q3 - Q1=62−52 = 10$.

Step4: Determine the lower and upper bounds

Lower bound $=Q1-1.5\times IQR=52-1.5\times10=52 - 15 = 37$. Upper bound $=Q3 + 1.5\times IQR=62+1.5\times10=62 + 15 = 77$.

Step5: Identify outliers

The value $15$ is less than the lower - bound $37$. So $15$ is an outlier.

Answer:

$15$