Question

Here are the numbers of calls received during

20

randomly chosen,

15

-minute time intervals at a customer support service.

1

,

4

,

6

,

6

,

8

,

9

,

11

,

11

,

11

,

12

,

13

,

13

,

14

,

14

,

17

,

17

,

18

,

18

,

21

,

23

(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 43. 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

Answer 1

(a) All the measures of central tendency exist for the dataset. Mean, Median and Mode can be computed from this dataset. The mean is 12.35, the median is 12.5 and the mode is 11.

(b) Since,the highest observation is changed and it is not the most frequent observation, so the mode will be unchanged. The median is not affected as the order of the dataset does not change. Only, the mean will be affected if 23 is replaced by 43.

(c) Since, the smallest observation is not mode, it will not be changed. However, the median and mean will be affected.

(d) Since, the mean of the dataset is close to the median, the dataset is roughly symmetrical.