Outlier Calculator

How to Calculate Outliers

Outliers are data points that significantly differ from other observations in a dataset. They can be identified using various methods, with the Interquartile Range (IQR) method being one of the most common.

Outlier Formula

The formulas for identifying outliers using the IQR method are:

• IQR = Q3 - Q1
• Lower Bound = Q1 - 1.5 * IQR
• Upper Bound = Q3 + 1.5 * IQR

Where:

• Q1 is the first quartile (25th percentile)
• Q3 is the third quartile (75th percentile)
• IQR is the Interquartile Range

Calculation Steps

1. Sort the dataset in ascending order.
2. Calculate Q1 and Q3.
3. Calculate the IQR by subtracting Q1 from Q3.
4. Calculate the Lower Bound and Upper Bound using the formulas above.
5. Identify outliers as any data points below the Lower Bound or above the Upper Bound.

Example

Let's calculate outliers for the dataset: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100

1. The dataset is already sorted.
2. Q1 = 2.75, Q3 = 7.25
3. IQR = 7.25 - 2.75 = 4.5
4. Lower Bound = 2.75 - 1.5 * 4.5 = -4
5. Upper Bound = 7.25 + 1.5 * 4.5 = 14
6. Outlier: 100 (above the Upper Bound)

Visual Representation

This diagram illustrates a box plot of our example dataset. The box represents the IQR, with the left edge at Q1 and the right edge at Q3. The whiskers extend to the minimum and maximum values within 1.5 * IQR of the quartiles. The red dot represents the outlier (100) that falls outside this range.