Q: A pie chart is used to display the results of a survey on favorite cake flavors. If 32 students prefer vanilla out of 170 total, what percentage of the pie chart should represent vanilla?

$$\frac{32}{170} \times 100 \approx 18.8\%$$

Question 1

Which of the following best describes the difference between qualitative and quantitative data?

Accepted Answer

Qualitative data consists of names or labels, while quantitative data consists of numerical values.

Question 2

A frequency distribution table is constructed for a data set with a minimum value of 12 and a maximum value of 67, using 7 classes. What is the class width?

Accepted Answer

$$\frac{67-12}{7} = 7.86$$, round up to 8

Question 3

Which type of graph is most appropriate for displaying the distribution of eye colors in a classroom?

Accepted Answer

Bar chart

Question 4

Given the following data set: $$\{5, 10, 14, 12, 3, 76\}$$, which measure of center is most affected by the outlier 76?

Accepted Answer

Mean

Question 5

A pie chart is used to display the results of a survey on favorite cake flavors. If 32 students prefer vanilla out of 170 total, what percentage of the pie chart should represent vanilla?

Accepted Answer

$$\frac{32}{170} 	imes 100 \approx 18.8\%$$

Question 6

Which of the following is the correct formula for the sample mean?

Accepted Answer

$$\bar{x} = \frac{\sum x}{n}$$

Question 7

A data set has the following values: $$\{20, 25, 30, 35, 40, 45, 50\}. $$What is the median?

Accepted Answer

35

Question 8

Which of the following best describes a histogram?

Accepted Answer

A graph that uses vertical bars to display frequencies of classes for quantitative data.

Question 9

If a data set is bell-shaped and symmetric, which measure of center is most appropriate to use?

Accepted Answer

Mean

Question 10

A sample of 500 books has a mean of 312 pages and a standard deviation of 26 pages. According to the Empirical Rule, what percentage of books have between 286 and 338 pages?

Accepted Answer

68\%

Question 11

Which of the following is the correct formula for the sample standard deviation?

Accepted Answer

$$s = \sqrt{\frac{\sum (x - \bar{x})^2$}{n-1}}$$

Question 12

A stemplot contains the row 2|0024555789. Which of the following lists all the data points in this row?

Accepted Answer

20, 20, 24, 25, 25, 25, 25, 27, 28, 29

Question 13

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile and the first quartile: $$IQR = Q_3$ - Q_1$

Question 14

A boxplot displays which of the following summaries?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 15

A frequency polygon is most similar to which other type of graph, and what is the main difference?

Accepted Answer

Histogram; frequency polygons use points connected by lines instead of bars.

Question 16

If a data set is highly skewed right, which measure of center is most resistant to outliers?

Accepted Answer

Median

Question 17

A time-series graph is best used for which type of data?

Accepted Answer

Data measured over time to show trends.

Question 18

A sample of 250 wait times at a restaurant has a mean of 8 minutes and a standard deviation of 2.5 minutes. According to the Empirical Rule, what is the range of wait times that contains approximately 95% of the data?

Accepted Answer

$$8 \pm 2 	imes 2.5 = 8 \pm 5 = [3, 13]$$ minutes

Question 19

Which of the following is true about the mode?

Accepted Answer

It is the most frequent value in a data set and can be used for both qualitative and quantitative data.

Descriptive Statistics: Measures of Center and Variation

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