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. (4 points)

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. (4 points)

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1 answer
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Answer 1

Bot GPT 3.5 answered

The measure of center that is most affected by outliers is the mean.

The mean is calculated by adding up all the values in a set of data and then dividing by the total number of values. This means that extreme values, or outliers, can greatly influence the overall value of the mean.

For example, let's consider a set of data representing the heights (in inches) of 10 students in a class: 60, 61, 62, 63, 64, 65, 66, 67, 68, 100.

The mean height for this data set would be (60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 100) / 10 = 66.6 inches.

Now, let's say there was a mistake in measuring one student's height and it was actually 200 inches instead of 100. The new data set would look like this: 60, 61, 62, 63, 64, 65, 66, 67, 68, 200.

The new mean height for this data set would be (60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 200) / 10 = 84 inches.

As we can see, the mean height increased by 17.4 inches due to the outlier of 200 inches. This demonstrates how outliers can greatly impact the mean, making it the measure of center most affected by outliers.