Outlier

Identifying Outliers Using Quartiles and Interquartile Range (IQR):

A common method to identify outliers is by using the interquartile range (IQR). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

Steps to Identify Outliers:

1. Calculate the IQR:

   • IQR = Q3 - Q1

2. Determine the lower and upper fences:

   • Lower fence = Q1 - 1.5 * IQR

   • Upper fence = Q3 + 1.5 * IQR

3. Identify outliers:

   • Any data point below the lower fence or above the upper fence is considered an outlier.

By using this method, we can effectively identify and potentially handle outliers in our dataset, leading to more accurate and reliable statistical analyses.

Example:

Consider the following dataset:

2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 100

1. Find the quartiles:

   • Q1 (25th percentile): 5

   • Q3 (75th percentile): 17

2. Calculate the IQR:

   • IQR = Q3 - Q1 = 17 - 5 = 12

3. Find the lower and upper fences:

   • Lower fence: Q1 - 1.5 * IQR = 5 - 1.5 * 12 = -13

   • Upper fence: Q3 + 1.5 * IQR = 17 + 1.5 * 12 = 35

4. Identify outliers:

   • Any value below -13 or above 35 is considered an outlier.

In this case, the value 100 is significantly larger than the upper fence, making it an outlier.