Which of the following descriptive statistics is least affected by adding an outlier to a data set?

(A) the mean

(B) the median

(C) the range

(D) the standard deviation

(E) all of the above

**Answer: B.** the median

Which of the following statements is incorrect?

(A) The median and the 1st quartile can be the same.

(B) The maximum and minimum value can be the same.

(C) The 1st and 3rd quartiles can be the same.

(D) The range and the IQR can be the same.

(E) None of the above.

**Answer: E. **None of the above.

The average annual returns over the past ten years for 20 utility stocks have the following statistics:

1st quartile = 7

Median = 8

3rd quartile = 9

Mean = 8.5

Standard deviation = 2

Range = 5

Give the five numbers that make up the five-number summary for this data set.

**Answer:** The five-number summary can’t be found.

Which of the following data sets has a mean of 15 and standard deviation of 0?

(A) 0, 15, 30

(B) 15, 15, 15

(C) 0, 0, 0

(D) There is no data set with a standard deviation of 0.

(E) Choices (B) and (C)

**Answer: B.** 15, 15, 15

Which of the following statements is true?

(A) Fifty percent of the values in a data set lie between the 1st and 3rd quartiles.

(B) Fifty percent of the values in a data set lie between the median and the maximum value.

(C) Fifty percent of the values in a data set lie between the median and the minimum value.

(D) Fifty percent of the values in a data set lie at or below the median.

(E) All of the above.

**Answer: E.** All of the above.

What is the range for the following data set:

1,2,8,9,7,4,1,1,3,2,3

**Possible Answers:**

1

4

8

2

**Correct answer:**8

Explanation:The range is the highest value number minus the lowest value number in a sorted data set:

1,2,8,9,7,4,1,1,3,2,3

We need to sort the data set:

1,1,1,2,2,3,3,4,7,8,9

range=9−1=8

### Example Question #3 : Calculating Range

What is the range for the following set:

63,49,68,59,29,62,46,5

**Possible Answers:**

63

−58

59

58

**Correct answer:**63

Explanation:The range is the difference between the highest and lowest number.

First sort the set:

5,29,46,49,59,62,63,68

68−5=63

### Example Question #1 : Calculating Range

Below is the stem-and-leaf display of a set of test scores.

45678∣∣∣∣∣∣∣2 54 4 7 70 1 2 2 4 5 8 8 93 5 5 87

What is the range of this set of scores?

**Possible Answers:**

40

52

45

42

50

**Correct answer:**45

Explanation:The range of a data set is the difference of the highest and lowest scores,

The numbers in the “stem” of this display represent tens digits of the test scores, and the numbers in the “leaves” represent the units digits. The highest and lowest scores represented are 87 and 42, so the range is their difference: 87−42=45.

### Calculating Range

Below is the stem-and-leaf display of a set of test scores.

45678∣∣∣∣∣∣∣2 54 4 7 70 1 2 2 4 5 8 8 93 5 5 87

What is the interquartile range of these test scores?

**Possible Answers:**

16

14

19

9

12

**Correct answer:**14