# in a sample with mean x = 12 and standard deviation

1. In a sample with mean x = 12 and standard deviation s = 3.5, a data point at 16.8 would have what sample z-score?

A. 4.8 B. We can’t know the answer without knowing the population mean μ and standard deviationσ. C. 1.4 D. 1.37

(16.8-12)/3.5 = 1.37

Answer D

2. Which of the following statements about interpreting standard deviation is true?

A. Chebyshev’s Rule can’t be applied unless the frequency distribution is mound-shaped and symmetric. The Empirical Rule can be applied to any data set, regardless of the shape of its frequency distribution.

B. The Empirical Rule can’t be applied unless the frequency distribution is mound-shaped and symmetric. Chebyshev’s Rule can be applied to any data set, regardless of the shape of its frequency distribution.

C. Neither Chebyshev’s Rule nor the Emprical Rule require any assumptions about the frequency distribution.

D. Neither the Empirical Rule nor Chebyshev’s Rule can be applied to data unless the frequency distribution is mound-shaped and symmetrical.

Answer B

3. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the median of this data sample?

A. There’s no median value.B. 9.25 C. 8 D. 7

Reorder the data: 3, 4, 6, 7, 9, 10, 14, 21

(7+9)/2 = 8

Answer C

4. Which of the following are parameters of a population?

A. σ and n B. μ and x C. μ and σ D. α and σ

These symbols need to be defined, but using normal conventions the answer is C

5. Which of the following statements is true about a stem-and-leaf plot?

A. It separates data at the decimal point, creating horizontal rows whose values are close together.

B. Stem-and-leaf plots are histograms whose bars have been arranged in decreasing order of frequency.

C. It involves creating columns of dots, one for each datum in the sample.

D. It uses vertical bars to illustrate a probability distribution.

Answer A is best, but not always correct

6. When a sample is taken from a larger population, this suggests that which of the following will be used?

A. Independent events B. Computation of a sample mean

C. Inferential statistics D. Descriptive statistics

Answers C and D are both suggested

7. When creating a histogram, it’s important to ensure that the classes of data satisfy which properties?

A. They must include each interval on the number line.

B. They must be all the same size.

C. They must be mutually exclusive and exhaustive.

D. No requirements are made; the individual creating the graph is free to choose any classes.

Answer C

8. To answer the question, refer to the following data.

Ten students were sampled at random from a student population. Each was asked how many courses he or she was planning on studying in the upcoming year. The following is a list of the reported data values: 1, 2, 2, 3, 4, 5, 5, 5, 5, 6

What is the standard deviation for the data values?

A. 2.84 B. 1.44 C. 2.56 D. 1.687

The correct answer is not given. Since the question states that the numbers are part of a sample, and the sample standard deviation is one of the 4 optional answers, I will assume the questioner wants the sample standard deviation.

Answer D

9. To answer the question, refer to the following data.

Ten students were sampled at random from a student population. Each was asked how many courses he or she was planning on studying in the upcoming year. The following is a list of the reported data values: 1, 2, 2, 3, 4, 5, 5, 5, 5, 6

What is the variance for the data values?

A. 1.687 B. 2.56 C. 1.6 D. 2.844

The correct answer is B, but to be consistent with the previous answer, the sample variance is 1.6865^{2} = 2.844. My guess is that the questioner thinks D is correct. The questioner seems to incorrectly think that the standard deviation and variance of a set of numbers depends on whether the numbers are part of a sample.

10. If there are an odd number of data values in a set, the median will be the

A. average of all of the values divided by the number of values in the set.

B. average of the two end values.

C. value that appears the greatest number of times.

D. value that appears in the center.

Again, all these answers are incorrect. Answer D is correct if the values are arranged in ascending or descending order.

11. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the range of this data sample?

A. 4 B. 18 C. 6 D. 10

21-3 = 18

Answer B

12. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the mean of this data sample?

A. There’s no mean value. B. 8 C. 7 D. 9.25

(4+14+6+9+21+3+7+10)/8 = 9.25

Answer D

13. Which of the following involves inferential statistics as opposed to descriptive statistics?

A. A local cable system, using a sample of 500 subscribers, estimates that 40 percent of its subscribers watch a premium channel at least once per day.

B. A class of 50 statistics students earned an average grade of 73.5.

C. The Alcohol, Tobacco and Firearms department reported that Houston had 1,791 registered gun dealers in 1997.

D. The city business office reported 35 building permits for new single-family housing units.

Answer A

14. What is the difference between a histogram and a bar chart?

A. The adjacent rectangles in a bar chart have a gap, while those for a histogram don’t.

B. A histogram reflects qualitative data, while the bar chart represents quantitative data.

C. The adjacent rectangles in a histogram have a gap, while those for a bar chart don’t.

D. A histogram and a bar chart both reflect qualitative data.

None of the options are correct.

15. A population is a collection of _______ about which we will measure certain characteristics or

properties, called _______.

A. data,numbers B.individuals, sample valuesC. experimental units, variablesD. people, traits

Answer C

LargeAirlines $4.36,6.19, -0.42,3.73,0.26,6.27 Small Airlines $1.60,-1.98,1.06,-0.21,-1.15 4.49,0.59,1.52,1.97,4.57,0.05

16. A study was conducted of the 12-month earnings per share for two categories of airline companies,with the result shown in the chart above.

Based on the data, which of the following statements is *correct?*

**A. **The large airlines have a mean earnings per share of 3.40, and the small airlines have a standard deviation of 2.01.

**B. **The large airlines have a variance of 4.04, and the small airlines have a variance of 8.30.

**C. **The large airlines have a standard deviation of 2.88, and the small airlines have a standard deviation of 4.04.

**D. **The large airlines have a mean earnings per share of 3.40, and the small airlines have a mean earnings per share of 1.22.

Once again there is a problem with the question because the mean, variance, and standard deviation can not be determined from a sample. I calculated the sample statistics below, and none of the options are correct.

Large airline sample average = (4.36+6.19-0.42+3.73+0.26+6.27)/6 = 3.40

Large airline sample variance = [4.36^{2}+6.19^{2}+0.42^{2}+3.73^{2}+0.26^{2}+6.27^{2}) – 6(3.40^{2})]/5 = 8.301

Large airline standard deviation = sqrt(8.301) = 2.88

Small airline mean = (1.60-1.98+1.06-0.21-1.15+4.49+0.59+1.52+1.97+4.57+0.05)/11 = 1.14

Small airline variance = 1.60^{2}+1.98^{2}+1.06^{2}+0.21^{2}+1.15^{2}+4.49^{2}+0.59^{2}+1.52^{2}+1.97^{2}+4.57^{2}+0.05^{2} – 11(1.14^{2}) = 4.233

Small airline standard deviation = sqrt(4.233) = 2.06

**17. **If a great many data values cluster to the left of a data distribution, which then tails off to the right, the distribution is referred to as

**A. **leftward skewed.**B. **rightward skewed.**C. **normal.**D. **uniform.

Answer B

**18. **Consider the following distribution:

Which of the following would you expect?

**A. **The mean is less than the median, and the median is less than the mode.

**B. **There’s no difference in the values of the mean, median, and mode.

**C. **The mean is greater than the median, and the median is greater than the mode.

**D. **The mean is greater than the mode, which in turn is greater than the median.

Incomplete question

**19. **A particular sample contains 50 data values. According to Chebyshev’s theorem, which of the following

is the number of values you would expect to fall within 3.0 standard deviations of the mean?

A.25 **B. **35 **C. **5 **D. **45

50(1 – 1/3^{2}) = 44.4

Answer D

**20. **Which type of plot takes quantitative data and forms classes out of it, thus turning it into qualitative data?

**A. **Histogram **B. **Dot plot **C. **Stem-and-leaf plot **D. **Pie chart

Answers A, B, and C

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