Multiple Choice Answers

1. Measures of dispersion:
a) provide information that allow comparisons between the spreads of two or more distributions.
b) cannot be calculated for grouped data.
c) convey information on how the data is clustered around the median.
d) All of the above

2. Please answer questions 2–7 using the following sample data.
13 29 41 60 89
14 26 53 7 14

What is the arithmetic mean of the data?
a) 34.6
b) 14
c) 50
d) 30.4

3. Based on the information in the chart in #2 (above), what is the median of the data?
a) 27.5
b) 14
c) 34.6
d) 51

4. Based on the information in the chart in #2 (above), what is the range of the data?
a) 14
b) 34.6
c) 82
d) 27.5

5. Based on the information in the chart in #2 (above), what is the mean deviation of the data?
a) 0
b) 10.5
c) 20.9
d) 209

6. Based on the information in the chart in #2 (above), what is the variance of the data?
a) 231
b) 616.2
c) 685.2
d) 1,197.2

7. Based on the information in the chart in #2 (above), what is the standard deviation of the data?
a) 0.2
b) 24.83
c) 26.18
d) 34.61

8. The coefficient of variation generally lies between:
a) -1 and +1.
b) -3 and +3.
c) 0% and 100%.
d) unlimited values.

9. The mean of a data set is 20 and s = 2. According to Chebyshev’s theorem, what is the percentage of values that lie within 3 standard deviations of the mean?
a) 11.1%
b) 68%
c) 88.9%
d) 96%

10. A non-normal population is determined to have a mean of 60 and a standard deviation of 4. Ninety-six percent of all observed values will occur in what range?
a) 52.16-67.84
b) 50-60
c) 48-72
d) 40-80

11. A study of hours devoted to a graduate course outside of classroom time generates a mean score of 90 with a standard deviation of 20. The mean age of the students was 31 with a standard deviation of 5 years. What is the relative dispersion of the two data sets?
a) 2.22%; 1.6%
b) 22.22%; 16.13%
c) 34.44%; 20%
d) Not calculable without additional data

12. Based on the empirical rules, what percent of the observations in a data set will lie beyond two standard deviations above the mean?
a) 2.5%
b) 5%
c) 68%
d) 95%

13. For a sample of engineers, the mean salary is $95,000 with a standard deviation of $30,000. The median value is $80,000. What is the relative shape of the distribution and coefficient of skewness?
a) Negatively skewed; -1.00
b) Negatively skewed; 1.00
c) Positively skewed; 1.50
d) Positively skewed; 3.00

14. Please answer questions 14–16 using the following sample data.
13 29 41 60 89
14 26 53 7 14

What is the first quartile?
a) 11.5
b) 13.75
c) 37
d) 50.75

15. Based on the information in the chart in #14 (above), what is the interquartile range?
a) 6
b) 39.5
c) 41
d) 44.25

16. Based on the information in the chart in #14 (above), what is the 90th percentile?
a) 9.9
b) 55.5
c) 86.1
d) 89

17. The interquartile range describes the:
a) lower 50% of observations.
b) lower 25% and upper 25% of observations.
c) middle 50% of observations.
d) upper 50% of observations

18. A survey of passengers on domestic flights revealed these miles:
Miles Flown Number of Passengers
100 up to 500 16
500 up to 900 41
900 up to 1,300 81
1,300 up to 1,700 11
1,700 up to 2,100 9
2,100 up to 2,500 6

What is the range (in miles)?
a) 2,499
b) 1,100
c) 2,400
d) 1,999

19. A box plot shows:
a) the mean and variance.
b) the relative symmetry of a distribution for a set of data.
c) the percentiles of a distribution.
d) nthe deciles of a distribution.

20. What statistics are needed to draw a box plot?
a) Minimum, maximum, median, first, and third quartiles
b) Median, mean, and standard deviation
c) A mean and a dispersion
d) A mean and a standard deviation