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

1) the mean is affected by outliers.

2) the mean is always a more accurate measure of center than the median.

3) removing an outlier from a data set will cause the standard deviation to increase.

4) if the data set's distribution is skewed, then 95%of its values will fall between two standard deviations of the mean.

5) if a data set's distribution to skewed to the right, its mean will be larger than its median.

1 and 5 are correct.

Step-by-step explanation:

1. The mean is affected by outliers. - TRUE

(the mean is the average so each of its values affect it.)

2. The mean is always a more accurate measure of center than the median. - FALSE

(the mean gives a better idea of the values while the the central values for normal distributions are described using the median value.)

3. Removing an outlier from a data set will cause the standard deviation to increase. - FALSE

(it makes the data set more normal by reducing the standard deviation, not increasing it.)

4. If the data set's distribution is skewed, then 95%of its values will fall between two standard deviations of the mean. - FALSE

(the 68-95-99.9 rule works for the normal distribution, but the skewed distribution.)

5. If a data set's distribution to skewed to the right, its mean will be larger than its median. - TRUE

(the mean is always pulled towards the direction of the skewness.)