Question

The Box-and-Whisker Plot represents the ages of 40 people who responded to a telephone survey.

Which statement is true about this data set?

A. About 50% of the respondents were at or between 40 and 67.5 years old.
B. The range of the data is 84 years.
C. The outlier is 28 years.
D. The mean is 51 years.

Answer 1

'A' is true; theoretically, 50% of the data items reside between the first and third quartiles (40 and 67.5)

Explanation:

Range is 84-28 which is 56

Median is 51

1.5 x Interquartile Range (IQR) = 1.5(67.5-40) which equals 41.25

Q1 is 40

Q1 - IQR = -1.25

Low outliers are below -1.25 - 41.25; there are not data items below -42

Answer 2

'A' is true; theoretically, 50% of the data items reside between the first and third quartiles (40 and 67.5)

Explanation:

Range is 84-28 which is 56

Median is 51

1.5 x Interquartile Range (IQR) = 1.5(67.5-40) which equals 41.25

Q1 is 40

Q1 - IQR = -1.25

Low outliers are below -1.25 - 41.25; there are not data items below -42