Question

The five number summary of a dataset was found to be: 45, 46, 51, 60, 66
An observation is considered an outlier if it is below:____________.
An observation is considered an outlier if it is above:____________.

Answer 1

Answer/Step-by-step explanation:

Given the five summary of a data set:

45 - min

46 - Q1

51 - Median

60 - Q3

66 - Max

Thus, any number less than $Q_1 - (1.5*IQR)$, or any number that is greater than $Q_3 + (1.5*IQR)$ would be considered an outlier.

The IQR of the data set = Q3 - Q1 = 60 - 46 = 14

Thus,

$Q_1 - (1.5*IQR) = 46 - (1.5*14) = 46 - 21 = 25$

Therefore, an observation is considered an outlier if it is below: 25.

$Q_3 + (1.5*IQR) = 60 + (1.5*14) = 60 + 21 = 81$

Therefore, an observation is considered an outlier if it is above: 81.