Math Portal
Introductory Statistics
Section 1.7 - Calculating Potential Outliers
Take a look at a set of data. (2, 3, 4, 4, 5, 6, 6, 6, 8, 10, 11, 12, and 30). Most of the numbers seem to be fairly well grouped except for 30. It seems to not quite fit in with the rest of the data. But is it an outlier? How can we tell?
We can calculate out a group of values that will tell us if any particular data point in a set is in fact an outlier. These groups are called fences. If any data falls outside the first group (called the inner fences) then the datum is considered a minor outlier. If the data falls outside the second value (called the outer fences) then the datum is considered a major outlier.
Calculate the Inner Fences - To calculate the inner fences we use the Interquartile Range (IQR) which is found by subtracting the 3rd quartile value from the 1st quartile value. We then multiply the IQR by 1.5 and then add it to the 3rd quartile and subtract it from the 1st quartile. Values that fall outside of the inner fences are considered outliers.
Example: Given the following data which (if any) are outliers: 23, 56, 73, 50, 2, 56, 45, 200?
Solution: We first calculate summary numbers - the median as 53, the first quartile as 28.5 and the third quartile as 68.75.
-> The IQR then is 40.25.
-> Multiply this result by 1.5 and we get 60.375.
-> The inner fences are (Lower) 28.5-60.375 = -31.875 and (Upper) as 68.75+60.375 = 129.125.
So 200 is considered an outlier!
Take a look at a set of data. (2, 3, 4, 4, 5, 6, 6, 6, 8, 10, 11, 12, and 30). Most of the numbers seem to be fairly well grouped except for 30. It seems to not quite fit in with the rest of the data. But is it an outlier? How can we tell?
We can calculate out a group of values that will tell us if any particular data point in a set is in fact an outlier. These groups are called fences. If any data falls outside the first group (called the inner fences) then the datum is considered a minor outlier. If the data falls outside the second value (called the outer fences) then the datum is considered a major outlier.
Calculate the Inner Fences - To calculate the inner fences we use the Interquartile Range (IQR) which is found by subtracting the 3rd quartile value from the 1st quartile value. We then multiply the IQR by 1.5 and then add it to the 3rd quartile and subtract it from the 1st quartile. Values that fall outside of the inner fences are considered outliers.
Example: Given the following data which (if any) are outliers: 23, 56, 73, 50, 2, 56, 45, 200?
Solution: We first calculate summary numbers - the median as 53, the first quartile as 28.5 and the third quartile as 68.75.
-> The IQR then is 40.25.
-> Multiply this result by 1.5 and we get 60.375.
-> The inner fences are (Lower) 28.5-60.375 = -31.875 and (Upper) as 68.75+60.375 = 129.125.
So 200 is considered an outlier!