Question

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.

Answer 1

The mean is affected by outliers. 
- TRUE - the mean is the average, so each value affects it.

The mean is always a more accurate measure of center than the median. 
- FALSE: Although the mean gives a better idea of the values, the center for Normal distributions is described using the median value. 

Removing an outlier from a data set will cause the standard deviation to increase.
- FALSE: Removing an outlier from a data set makes the data more Normal, reducing the standard deviation, not increasing it. 

If a 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 a bell-curve distribution, a.k.a. a Normal distribution, not a skewed distribution.

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 in the direction of the skewness.