Bids were placed in a silent auction for a sword reputed to have been used at the Battle of Hastings and worth a reported

$20,000

. The respective bids (in thousands of dollars) placed by the

20

bidders were as follows.

3

,

9

,

12

,

12

,

14

,

14

,

16

,

16

,

17

,

17

,

18

,

18

,

18

,

19

,

21

,

21

,

21

,

21

,

21

,

23

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8

6

4

2

0

Frequency

1

1

4

8

6

0

5

10

15

20

25

Bid (in thousands of dollars)

(a)Which measures of central tendency do not exist for this data set? Choose all that apply.

Mean

Median

Mode

None of these measures

(b)Suppose that the measurement 23 (the largest measurement in the data set) were replaced by 41. 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)The relative values of the mean and median for the original data set are typical of data that have a significant skew to the left. What are the relative values of the mean and median for the original data set? Choose only one.

Mean is greater

Median is greater

Cannot be determined