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 dividing by the total number of values, so outliers can greatly affect the sum and therefore the mean.
For example, let's consider the following data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100
The mean of this data set is (1+2+3+4+5+6+7+8+9+100)/10 = 14.5
Now, if we add an outlier to the data set like 1000, the mean will become (1+2+3+4+5+6+7+8+9+100+1000)/11 = 105.9
As we can see, the outlier greatly affected the mean, pulling it towards a higher value. The median and mode, on the other hand, would not be affected as much by this outlier.
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)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
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