Q: A pie chart is constructed to show the distribution of degrees earned in a university. If 1,037 out of 4,072 degrees are in Science, what is the central angle for the Science sector?

$$\frac{1,037}{4,072} \times 360 = 91.7$$^{\circ}$$

Q: If a data set has a mean of 50 and a standard deviation of 5, what is the coefficient of variation (CV) for the population?

$$CV = \frac{5}{50} \times 100\% = 10\%$$

Q: Using the IQR method, which value is an outlier in the following data set: $$Q_1 = 15$, Q_3$ = 35$$, and a data entry of 60?

60 is an outlier because $$60 \u003e Q_3$ + 1.5 \times IQR$$

Q: A frequency distribution has midpoints 10, 20, 30 and frequencies 2, 3, 5. What is the mean of the distribution?

$$\frac{(10 \times 2) + (20 \times 3) + (30 \times 5)}{2 + 3 + 5} = \frac{20 + 60 + 150}{10} = \frac{230}{10} = 23$$

Question 1

A frequency distribution table is constructed for a set of exam scores. The lowest score is 42 and the highest is 98. If you want to create 7 classes, what is the class width you should use?

Accepted Answer

$$\frac{98 - 42}{7} = 8 ($$rounded up to 9)

Question 2

Which of the following statements about frequency histograms is TRUE?

Accepted Answer

Consecutive bars must touch because the data is continuous.

Question 3

A pie chart is constructed to show the distribution of degrees earned in a university. If 1,037 out of 4,072 degrees are in Science, what is the central angle for the Science sector?

Accepted Answer

$$\frac{1,037}{4,072} 	imes 360 = 91.7$$^{\circ}$$

Question 4

Which measure of central tendency is most affected by outliers in a data set?

Accepted Answer

Mean

Question 5

Given the following data set: 2, 4, 6, 8, 10, what is the median?

Accepted Answer

6

Question 6

A sample of test scores has a mean of 75 and a standard deviation of 8. What is the z-score for a test score of 91?

Accepted Answer

$$z = \frac{91 - 75}{8} = 2$$

Question 7

Which distribution is described as having all entries or classes with equal or approximately equal frequencies?

Accepted Answer

Uniform distribution

Question 8

If a data set has a mean of 50 and a standard deviation of 5, what is the coefficient of variation (CV) for the population?

Accepted Answer

$$CV = \frac{5}{50} 	imes 100\% = 10\%$$

Question 9

A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 20$$

Question 10

Using the IQR method, which value is an outlier in the following data set: $$Q_1 = 15$, Q_3$ = 35$$, and a data entry of 60?

Accepted Answer

60 is an outlier because $$60 \u003e Q_3$ + 1.5 	imes IQR$$

Question 11

A sample has the following values: 5, 7, 9, 11. What is the sample variance?

Accepted Answer

$$s^2$$ = \frac{$$(5-8)^2$$ + $$(7-8)^2$$ + $$(9-8)^2$$ + $$(11-8)^2$$}{4-1} = \frac{9 + 1 + 1 + 9}{3} = \frac{20}{3} \approx 6.67$$

Question 12

According to Chebychev’s Theorem, what proportion of data lies within 3 standard deviations of the mean?

Accepted Answer

$$1 - \frac{1}{3^2$} = 1 - \frac{1}{9} = \frac{8}{9}$$

Question 13

A frequency distribution has midpoints 10, 20, 30 and frequencies 2, 3, 5. What is the mean of the distribution?

Accepted Answer

$$\frac{(10 	imes 2) + (20 	imes 3) + (30 	imes 5)}{2 + 3 + 5} = \frac{20 + 60 + 150}{10} = \frac{230}{10} = 23$$

Question 14

Which of the following best describes a scatter plot?

Accepted Answer

A graph of ordered pairs showing the relationship between two quantitative variables.

Question 15

If a data set is skewed right, which statement is correct?

Accepted Answer

The mean is to the right of the median.

Question 16

A box-and-whisker plot requires which of the following values?

Accepted Answer

Minimum, $$Q_1$$, Median ($$Q_2$$), $$Q_3$$, Maximum

Question 17

What is the percentile for a data entry that is the 15th value in a data set of 60 values?

Accepted Answer

$$\frac{14}{60} 	imes 100 = 23.3\%$$

Question 18

Which of the following is NOT a measure of variation?

Accepted Answer

Mode

Descriptive Statistics: Frequency Distributions, Graphs, and Measures of Central Tendency, Variation, and Position

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