Answer:

Interquartile range: 49.5
Outlier(s): 93, 131, 830
Potential outlier(s): none

See the outliers and potential outliers highlighted in the sorted data set here:
93, 131, 505, 530, 538, 544, 545, 551, 553, 563, 567, 576, 580, 587, 590, 646, 830

Solution:

The interquartile range, IQR, is the difference between Q3 and Q1. In this data set, Q3 is 583.5 and Q1 is 534. Subtract Q1, 534, from Q3, 583.5. $$ IQR = 583.5 - 534 = 49.5 $$ You can use the 5 number summary calculator to learn steps on how to manually find Q1 and Q3.

To find outliers and potential outliers in the data set, we first need to calculate the value of the inner fences and outer fences. The inner fences are defined by: $$ Q1 - (1.5 \cdot IQR) \text{ and } Q3 + (1.5 \cdot IQR) $$ For this data set: $$ 534 - (1.5 \cdot 49.5) \text{ and } 583.5 + (1.5 \cdot 49.5) $$ $$ \text{Inner fences: } 459.75 \text{ and } 657.75$$

The outer fences are defined by: $$ Q1 - (3 \cdot IQR) \text{ and } Q3 + (3 \cdot IQR) $$ For this data set: $$ 534 - (3 \cdot 49.5) \text{ and } 583.5 + (3 \cdot 49.5) $$ $$ \text{Outer fences: } 385.5 \text{ and } 732 $$

The inner and outer fences are listed below. Potential outliers are any values in our data set that fall between the inner fences and outer fences, inclusive. Outliers are any values that fall outside of the outer fences.

If there are any outliers in this data set, they will either be less than 385.5 or greater than 732. Potential outliers will be between 385.5 and 459.75, inclusive or between 657.75 and 732, inclusive.

In this data set, the outlier(s) is/are: 93, 131, 830 In this data set, there are no potential outliers.