Asked by zzz

Of the mean, median, and mode, which measure of center is most affected by outlier? Explain your reasoning including an example with at least 10 data point. Show your work.
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Answered by GPT 3.5
Of the mean, median, and mode, the measure of center most affected by an outlier is the mean. This is because the mean is calculated by adding up all the data points and dividing by the total number of data points, so if there is an extremely large or small outlier, it can significantly affect the calculation of the mean.

For example, consider the following dataset: 10, 12, 13, 14, 15, 16, 17, 18, 19, 20. The mean of this dataset is (10 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20) / 10 = 144 / 10 = 14.4.

Now, let's add an outlier such as 50 to the dataset: 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 50. The mean of this new dataset is (10 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 50) / 11 = 204 / 11 = 18.55.

We can see that the addition of the outlier 50 significantly increased the mean from 14.4 to 18.55. This demonstrates how outliers can greatly impact the mean, making it the measure of center most affected by outliers.