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Chapter 3: Problem 2

Briefly explain the meaning of an outlier. Is the mean or the median a better measure of central tendency for a data set that contains outliers? Illustrate with the help of an example.

Short Answer

Expert verified
An outlier is a data point that significantly varies from other observations. It affects the mean, pulling it towards the outlier, hence not accurately representing the central tendency in a dataset with outliers. The median, however, remains unaffected by the outliers, making it a better measure of central tendency for datasets with outliers. An example: for the dataset \(2, 3, 4, 4, 9, 40\), the mean is \(10.33\) and median is \(4.5.\)

Step by step solution

01

Define an Outlier

An outlier is a data point that differs significantly from other observations in a dataset. It can occur due to variability in the data or due to experimental errors. Outliers can distort the interpretation and analyses of the data.
02

Mean and Outliers

The mean is the average of all numbers in the dataset. Its value can be heavily influenced by outliers. If there are extremely high or low outliers, they can drag the mean towards them, leading to an inaccurate representation of the central tendency.
03

Median and Outliers

The median is the middle number of a sorted dataset. Whether outliers are extremely high or low, they do not affect the value of the median. It provides a better measure of central tendency when the dataset contains outliers.
04

Illustrate with Example

Consider a dataset: \(2, 3, 4, 4, 9, 40\). The mean is \(10.33\), pulled upwards by the outlier '40'. On the other hand, the median value \(4.5\) less distorted by the outlier and gives a better representation of the central tendency.

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