2 22 27 31 36 51 57 57 60 62 62 62 73 77 83 9

2 , 22 , 27 , 31 , 36 , 51 , 57 , 57 , 60 , 62 , 62 , 62 , 73 , 77 , 83 , 95 , 99 , 104 , 105 , 127 , 153 , 162 , 197

(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 197 (the largest measurement in the data set) were replaced by 246. 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 largest 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 62 (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 62.

Thus, OPTION A: MEAN.

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c.

By the same reasoning, the mean will change again.

As the last term is removed, ordering differed and the median may change. However, it so happened that the 2 new middle terms are both 62, which is also the old median. Thus, THE MEDIAN DID NOT CHANGE.

The mode remains at 55.

Thus there is one answer: MEAN. [ANSWER]

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D.

We see that there is a longer list to the right of the mode (62) than to its right.

Thus, it is POSITIVELY SKEWED. [ANSWER]