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Chapter 3: Problem 3

Using an example, show how outliers can affect the value of the mean.

Short Answer

Expert verified
In this example, the mean value increased from 6.8 to 14 when the outlier (50) was included in the dataset, demonstrating how outliers can affect the value of the mean.

Step by step solution

01

Setup the Example Set

Let's consider a simple example dataset: 2, 4, 7, 9, 12. The total count \( n \) is 5.
02

Calculate the Mean without an Outlier

First, calculate the mean without an outlier. The mean \( M \) is calculated as the sum of all values \( \Sigma x \) divided by the total count \( n \). So \( M = \frac{\Sigma x}{n} = \frac{2+4+7+9+12}{5} = 6.8 \)
03

Introduce an Outlier

Now, an outlier is introduced to the dataset: 2, 4, 7, 9, 12 and 50. The outlier in this case is 50, a number significantly higher than the others. The total count \( n \) is now 6.
04

Calculate the Mean with the Outlier

Next, calculate the mean with the outlier. The mean \( M \) will now be \( M = \frac{\Sigma x}{n} = \frac{2+4+7+9+12+50}{6} = 14 \)
05

Analyze the Result

The mean value significantly changed from 6.8 to 14, when the outlier was included. This demonstrates the effect of an outlier on the mean value of a dataset.

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