Question

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

Answer 1

A. True. The mean is larger than normal if there is a very large outlier (to the right of the main cluster). The mean is smaller than normal if there is a very small outlier (to the left of the main cluster)

B. False. The outliers skew the true value of the mean. If you are talking about a trimmed mean, then you might have an accurate mean. For situations involving outliers, its best to use the median. One example is with home prices. Very rich homes selling upwards of 10 million dollars will skew the prices of homes that sell for hundreds of thousands of dollars. The mean home price will be very large because of the rich homes, which is why you hear of "median home price" instead of "mean home price" whenever there are housing reports.

C. False. The standard deviation will go down. The standard deviation measures how spread out the data is (more or less). The outlier makes the overall data set more spread out, leading to a higher standard deviation. Once you remove the outlier, the standard deviation will go down as the data set is more clumped together.

D. False. This only applies to normally distributed data (on a bell shaped curve) which is symmetrical about the mean. Skewed data sets will break this rule. 

E. True. The phrase "skewed to the right" indicates that there is a very large outlier pulling the right tail longer than it should be. In other words, it has a very long tail on the right. The large outlier will enlarge the mean, pulling it to the right as well. The median will stay in place. As a result, the mean is larger than the median. This is similar in theme to what choice A is saying above.

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In summary, the true answers are
Choice A
Choice E
There are two true answers