Which of the following statements are true? check all that apply.

-the mean is affected by outliers.
-the mean is always a more accurate measure of center than the median.
-removing an outlier from a data set will cause the standard deviation to increase.
-if a data set’s distribution is skewed, then 95% of its values will fall between two standard deviations of the mean.
-if a data set’s distribution to skewed to the right, its mean will be larger than its median.

These are true:
-The mean is affected by outliers. (every number in a set affects the mean)

-If a data set’s distribution is skewed, then 95% of its values will fall between two standard deviations of the mean. (we know from Chebyshev's Theorem that this is true for any set, skewed or not)

The rest are not true because:
-The mean is always a more accurate measure of center than the median. (there can be an extremely large outlier, imagine data set [1,2,3,4,9845}, the median is a more accurate measure of the center)

-Removing an outlier from a data set will cause the standard deviation to increase. (an outlier raises the variance which raises the standard deviation, so removing an outlier lowers the standard deviation)

-If a data set’s distribution is skewed to the right, its mean will be larger than its median. (while this is generally true, there can be sets of numbers that don't hold true here)

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