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Question
Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The measure of center that is most affected by outliers is the mean. The mean is calculated by adding up all the data points and dividing by the total number of data points. Outliers can greatly influence the mean because they can greatly increase or decrease the sum of all the data points, thereby affecting the calculated average. In the presence of outliers, the mean may not accurately represent the central tendency of the data set.

For example, consider the following data set:
10, 12, 13, 15, 16, 17, 18, 19, 20, 100

The mean of this data set is (10+12+13+15+16+17+18+19+20+100)/10 = 24

Now, let's remove the outlier (100) from the data set:
10, 12, 13, 15, 16, 17, 18, 19, 20

The mean of this new data set is (10+12+13+15+16+17+18+19+20)/9 = 15.555...

As we can see, the presence of the outlier greatly affected the mean of the original data set, causing it to be significantly higher. This demonstrates how outliers can skew the mean and make it a less reliable measure of center when dealing with skewed data sets.

Answer 2

shorten it

Answer 3

[AI-generated answer — Bot GPT 3.5]

The mean is the measure of center that is most affected by outliers because outliers can greatly increase or decrease the sum of all the data points, thereby affecting the calculated average. In the presence of outliers, the mean may not accurately represent the central tendency of the data set.

For example, in a data set of 10, 12, 13, 15, 16, 17, 18, 19, 20, and 100, the mean is 24. Removing the outlier (100) from the data set changes the mean to 15.555..., showing how outliers can greatly impact the mean.