Outlier/Interquartile Range Calculator
Answer:
Interquartile range: 109
Outlier(s):
100
Potential outlier(s):
246
See the outliers and potential outliers highlighted in the sorted data set here:
100, 246, 507, 554, 568, 580, 587, 611, 622, 623, 632, 648, 676, 677, 684, 684, 695, 839
Solution:
The interquartile range, IQR, is the difference between Q3 and Q1. In this data set, Q3 is 677 and Q1 is 568. Subtract Q1, 568, from Q3, 677. $$ IQR = 677 - 568 = 109 $$ 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: $$ 568 - (1.5 \cdot 109) \text{ and } 677 + (1.5 \cdot 109) $$ $$ \text{Inner fences: } 404.5 \text{ and } 840.5$$
The outer fences are defined by: $$ Q1 - (3 \cdot IQR) \text{ and } Q3 + (3 \cdot IQR) $$ For this data set: $$ 568 - (3 \cdot 109) \text{ and } 677 + (3 \cdot 109) $$ $$ \text{Outer fences: } 241 \text{ and } 1004 $$
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 |
| 241 | 404.5 | 840.5 | 1004 |
If there are any outliers in this data set, they will either be less than 241 or greater than 1004. Potential outliers will be between 241 and 404.5, inclusive or between 840.5 and 1004, inclusive.
In this data set, the outlier(s) is/are:
100
In this data set, the potential outlier(s) is/are:
246