Outlier Formula

What is Outlier Formula? 

Outliers are data points with extreme values. We can use the outlier formula to discover outliers in a data set. The best and brightest persons are referred regarded be outliers in the literary world. Malcolm Gladwell's non-fiction book 'Outliers' debuted as the number one best seller on the New York Times best-seller list. Outliers, according to Malcolm, are people who have outstanding brains, and enormous riches, and are different from the norm. For more Maths formulas click on the main page. 

Outliers are data points with extreme values.

Examples of Outlier Formula

For a data set containing 1, 18, 24, 31, 37, 39, 31, 42, 58, 55, and 85 The numbers 1 and 85 are outliers in the above number line because they are at the extremes. The outliers are members of the group, but they are isolated from the others. The issue with outliers is that they cause an imbalance in the data collection, hence they are usually deleted. Also, an outlier can appear in a data set due to inaccuracy.

Consider the data: 71 + 72 + 78 + 70 + 8 + 72 + 71 + 79

Let's calculate the mean to understand how the outlier affects the results.

Here, the datapoint 7, is an outlier.

  • Mean (with outlier) = (71 + 72 + 78 + 70 + 8 + 72 + 71 + 79)/8 = 521/8 = 65.1
  • Mean (without an outlier) = (71 + 72 + 78 + 70 + 8 + 72 + 71 + 79)/7 = 514/7 = 73.4

We can now see how the outlier causes a variation in the data's mean value.

Let's first study quartiles and interquartile range before moving on to finding the outlier.

First Quartile Q1: The first quartile is defined as the midpoint of the first half of the data.

Second Quartile Q2: The second quartile is represented by the data's mid-value or median.

Third Quartile Q3: The third quartile is defined as the midpoint of the second half of the data.

The formula for Outliers (Turkey Method)

Outliers are found using Turkey's approach, which is a mathematical procedure. The points beyond the upper border of Q3 +1.5 IQR and the bottom boundary of Q1 - 1.5 IQR are considered outliers using the Turkey technique. Outlier fences are the names given to these types of borders.

  • Upper~Fence = Q3 +1.5 IQR
  • Lower~Fence = Q1 - 1.5 IQR

Outliers are data points in this box plot that are beyond upper & lower fences.

Outlier Formula

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Outlier Formula
Outlier Formula

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