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)
The median is the measure of center that is most affected by outliers. The reason for this is that the median is the middle value when the data set is arranged in order, and outliers can increase or decrease the value of the middle point.
For example, consider the following data set:
2, 3, 4, 5, 6, 7, 8, 9, 10, 200
The mean of this data set is 34.4, the mode is not relevant as there are no repeating values, and the median is 6.5. The outlier, 200, in this case greatly affects the median, pulling it towards the right end of the data set. If we were to remove the outlier and recalculate the median, it would be 5.5. This shows how one extreme value can have a significant impact on the median, making it the measure of center that is most affected by outliers.
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I apologize if my response was not helpful or incorrect. Can you please clarify which part of my response you believe is incorrect, so I can provide a more accurate answer?
The measure of center that is most affected by outliers is the mean.
The mean is calculated by summing all the data points and dividing by the total number of data points. Since the mean includes all the data points in its calculation, the inclusion of extreme values can heavily impact its value.
For example, let's consider the following set of 10 data points representing the monthly salaries of a group of employees at a small company:
{3000, 4000, 4000, 4500, 4700, 5000, 5000, 5500, 6000, 75000}
If we calculate the mean of this data set, we get:
Mean = (3000 + 4000 + 4000 + 4500 + 4700 + 5000 + 5000 + 5500 + 6000 + 75000) / 10 = 25500 / 10 = 2550
However, we can see that there is one extreme outlier in this data set, the salary of 75000. This outlier significantly skews the mean, causing it to be much larger than the rest of the values.
In contrast, the median and mode are less affected by outliers. The median is the middle value when the data set is arranged in ascending or descending order. In this example, the median salary is 5000. The mode is the value that appears most frequently, and in this case, it is also 5000.
Both the median and mode provide a more representative measure of the central tendency of the data without being influenced too much by extreme values.