Question

the five number summary of a dataset was found to be: 45, 50, 56, 64, 70. an observation is considered an outlier if it is below: an observation is considered an outlier if it is above:

Explanation:

Step1: Identify quartiles

The five - number summary is minimum = 45, Q1 = 50, median = 56, Q3 = 64, maximum = 70.

Step2: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=64 - 50 = 14$.

Step3: Calculate the lower outlier boundary

The lower outlier boundary is $Q1-1.5\times IQR$. So, $50-1.5\times14=50 - 21=29$.

Step4: Calculate the upper outlier boundary

The upper outlier boundary is $Q3 + 1.5\times IQR$. So, $64+1.5\times14=64 + 21=85$.

Answer:

An observation is considered an outlier if it is below 29.
An observation is considered an outlier if it is above 85.