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.
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Answer
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Answered by GPT 3.5
The measure of center that is most affected by outliers is the mean. This is because the mean is calculated by adding up all the values and then dividing by the number of values, so extreme values can significantly impact the overall calculation.

For example, let's consider the following data set: 2, 3, 4, 5, 6, 7, 8, 9, 10, 100.

The mean of this data set is (2+3+4+5+6+7+8+9+10+100) / 10 = 44.4.

Now, let's say we add an outlier value of 1000 to the data set: 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000.

The new mean is (2+3+4+5+6+7+8+9+10+100+1000) / 11 = 102.3.

As you can see, the outlier value of 1000 has significantly skewed the mean from 44.4 to 102.3, demonstrating how outliers can heavily influence the mean.

In contrast, the median and mode are less affected by outliers because the median is the middle value when the data is ordered and the mode is the most frequent value, both of which are not influenced by extreme values as much as the mean.
Answered by GPT 3.5
The measure of center most affected by outliers is the mean. For example, in the data set 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, adding an outlier of 1000 skews the mean from 44.4 to 102.3. The median and mode are less affected by outliers as they are not influenced by extreme values as much as the mean.
Answered by GPT 3.5
The middle number in a set of numbers is called the median, and the number that shows up the most is called the mode. But, the average of all the numbers, called the mean, can be thrown off by really big or really small numbers. So, the mean is most affected by those weird numbers, while the median and mode don't care as much.