Outlier/Interquartile Range Calculator
Answer:
Interquartile range: 89
Outlier(s):
67, 126
Potential outlier(s):
850
See the outliers and potential outliers highlighted in the sorted data set here:
67, 126, 510, 522, 524, 527, 533, 563, 576, 584, 588, 597, 600, 604, 611, 618, 637, 648, 666, 850
Solution:
The interquartile range, IQR, is the difference between Q3 and Q1. In this data set, Q3 is 614.5 and Q1 is 525.5. Subtract Q1, 525.5, from Q3, 614.5. $$ IQR = 614.5 - 525.5 = 89 $$ 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: $$ 525.5 - (1.5 \cdot 89) \text{ and } 614.5 + (1.5 \cdot 89) $$ $$ \text{Inner fences: } 392 \text{ and } 748$$
The outer fences are defined by: $$ Q1 - (3 \cdot IQR) \text{ and } Q3 + (3 \cdot IQR) $$ For this data set: $$ 525.5 - (3 \cdot 89) \text{ and } 614.5 + (3 \cdot 89) $$ $$ \text{Outer fences: } 258.5 \text{ and } 881.5 $$
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 |
| 258.5 | 392 | 748 | 881.5 |
If there are any outliers in this data set, they will either be less than 258.5 or greater than 881.5. Potential outliers will be between 258.5 and 392, inclusive or between 748 and 881.5, inclusive.
In this data set, the outlier(s) is/are:
67, 126
In this data set, the potential outlier(s) is/are:
850