Question

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

Answer 1

Answer:

(A) and (D)

Step-by-step explanation:

The true statements are:

(A) The mean is affected by outliers (because presence of outliers always affect the mean of the data set).

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

The not true statements are:

(B) The mean is always a more accurate measure of center than the median. (As there can be an extremely large outlier, For example consider the set {1,2,3,4,9845}, the median is a more accurate measure of the center).

(C) Removing an outlier from a data set will cause the standard deviation to increase. (This is because an outlier raises the variance which raises the standard deviation, thus removing an outlier lowers the standard deviation).

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

Answer 2

Answer:

Step-by-step explanation: