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 answer is clear and correct. The answer shows that the student used problem-solving skills and reasoning. All work is shown or explained.

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) The answer is clear and correct. The answer shows that the student used problem-solving skills and reasoning. All work is shown or explained.

Answer 1

The measure of center that is most affected by outliers is the mean. Outliers are extreme values that are significantly higher or lower than the rest of the data points, causing the mean to be pulled in the direction of the outlier.

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 calculated by adding all the numbers together and dividing by the total number of data points:
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 100) / 10 = 45.5

So, the mean of this data set is 45.5. However, this mean is heavily influenced by the outlier, 100. If we remove the outlier from the data set, the mean becomes:
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9 = 5.89

As we can see, the mean without the outlier is significantly different from the mean with the outlier, demonstrating that the mean is most affected by outliers.

Answer 2

make it shorter plss

Answer 3

The measure of center most affected by outliers is the mean. Outliers can greatly skew the mean because it involves adding up all the values and dividing by the total number of data points. For example, in the data set 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, the mean is 45.5. Removing the outlier 100, the mean drastically changes to 5.89, showing the impact of outliers on the mean.

Answer 4

is this: The measure of center most affected by outliers is the mean. part of the math work?

Answer 5

No, the phrase "The measure of center most affected by outliers is the mean" is not part of the math work. It is an introductory statement that sets the context for the explanation that follows. The mathematical work begins with the calculation of the mean and its comparison with and without the outlier in the provided example.