bmaggie

Which of the following statements regarding skewness is least accurate?

A) A distribution that is not symmetrical has skew not equal to zero.

B) In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean.

C) A positively skewed distribution is characterized by many small losses and a few extreme gains.

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For a normal distribution, the mean will be equal to its median and 95% of all observations will fall within plus or minus two standard deviations of the mean. For a skewed distribution, because it is not symmetrical, this may not be the case. Chebyshev’s inequality tells us that at least 75% of observations will lie within plus or minus two standard deviations from the mean.

bmaggie

A distribution with a mode of 10 and a range of 2 to 25 would most likely be:

A) normally distributed.

B) positively skewed.

C) negatively skewed.

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The distance to the left from the mode to the beginning of the range is 8. The distance to the right from the mode to the end of the range is 15. Therefore, the distribution is skewed to the right, which means that it is positively skewed.