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Outlier/Interquartile Range Calculator

Answer:

Interquartile range: 101.5
Outlier(s): 81, 171
Potential outlier(s): 804

See the outliers and potential outliers highlighted in the sorted data set here:
81, 171, 510, 521, 525, 530, 537, 559, 561, 577, 587, 589, 597, 602, 612, 646, 652, 675, 676, 804


Solution:

The interquartile range, IQR, is the difference between Q3 and Q1. In this data set, Q3 is 629 and Q1 is 527.5. Subtract Q1, 527.5, from Q3, 629. $$ IQR = 629 - 527.5 = 101.5 $$ 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: $$ 527.5 - (1.5 \cdot 101.5) \text{ and } 629 + (1.5 \cdot 101.5) $$ $$ \text{Inner fences: } 375.25 \text{ and } 781.25$$

The outer fences are defined by: $$ Q1 - (3 \cdot IQR) \text{ and } Q3 + (3 \cdot IQR) $$ For this data set: $$ 527.5 - (3 \cdot 101.5) \text{ and } 629 + (3 \cdot 101.5) $$ $$ \text{Outer fences: } 223 \text{ and } 933.5 $$

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.

Outliers Outer fence Inner fence Inner fence Outer fence Outliers
223 375.25 781.25 933.5

If there are any outliers in this data set, they will either be less than 223 or greater than 933.5. Potential outliers will be between 223 and 375.25, inclusive or between 781.25 and 933.5, inclusive.

In this data set, the outlier(s) is/are: 81, 171
In this data set, the potential outlier(s) is/are: 804