11 16 18 21 23 37 38 38 45 46 46 50 52 55 55

11 , 16 , 18 , 21 , 23 , 37 , 38 , 38 , 45 , 46 , 46 , 50 , 52 , 55 , 55 , 55 , 56 , 63 , 66 , 66 , 74 , 79 , 81 , 82 , 86

(a) For these data, which measures of central tendency take more than one value? Choose all that apply.
Mean
Median
Mode
None of these measures
(b) Suppose that the measurement 86 (the largest measurement in the data set) were replaced by 95. Which measures of central tendency would be affected by the change? Choose all that apply.
Mean
Median
Mode
None of these measures
(c) Suppose that, starting with the original data set, the smallest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.
Mean
Median
Mode
None of these measures
(d) Which of the following best describes the distribution of the original data? Choose only one.
Negatively skewed
Positively skewed
Roughly symmetrical

Solution

A.

The mean and median are always unique.

The mode can make more than one value, so we will see.

The mode here is 55 (3 times). There\'s no other.

Thus, the answer is D. NONE OF THE MEASURES. [ANSWER]

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B.

Only the mean gets affected as it is affected by the sum.

The median relies only on order, and mode remains 55.

Thus, OPTION A: MEAN.

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c.

By the same reasoning, the mean will change again.

As the first term is removed, ordering differed and the median changed.

The mode remains at 55.

Thus there are two answers: MEAN AND MEDIAN. [ANSWERS]

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D.

We see that there is a longer list to the left of the mode (55) than to its right.

Thus, it is NEGATIVELY SKEWED. [ANSWER]