Q: A sample of 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 that contains approximately 95% of the data?

$$8 \pm 2 \times 2.5 = 3 to$$ $$13$$ minutes

Question 1

Which of the following best describes the formula for the sample mean $$\bar{x}$$?

Accepted Answer

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

Question 2

A sample of home prices (in thousands of dollars) is: 275, 229, 850, 240, 305, 287, 310, 342. Which measure of center is most representative of the data, and why?

Accepted Answer

The median, because the data contains an outlier (850) that skews the mean.

Question 3

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

Accepted Answer

Mean

Question 4

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

Accepted Answer

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

Question 5

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 6

Which of the following statements about the median is TRUE?

Accepted Answer

The median is resistant to outliers.

Question 7

A histogram of college credits per semester is shown. If the data is skewed right, which measure of center is likely to be greater?

Accepted Answer

Mean

Question 8

Given the stemplot below, what is the mode of the data?

Accepted Answer

5

Question 9

A sample of 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 that contains approximately 95% of the data?

Accepted Answer

$$8 \pm 2 	imes 2.5 = 3 to$$ $$13$$ minutes

Question 10

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

Accepted Answer

The difference between the third quartile (Q3) and the first quartile (Q1)

Question 11

A boxplot displays which of the following?

Accepted Answer

The five-number summary: minimum, Q1, median, Q3, maximum

Question 12

If a data set is bimodal, what does this mean?

Accepted Answer

There are two values that occur most frequently.

Question 13

A student calculates the range of song lengths as 2.3 to 4.7 minutes. Using the range rule of thumb, estimate the standard deviation.

Accepted Answer

$$(4.7 - 2.3)/4 = 0.6$$ minutes

Question 14

Which of the following is NOT a property of the mean?

Accepted Answer

It is resistant to outliers.

Question 15

In a normal distribution, what percentage of data falls within one standard deviation of the mean?

Accepted Answer

68%

Question 16

A data set has a mean of 50 and a standard deviation of 5. According to the range rule of thumb, what value would be considered significantly low?

Accepted Answer

40 or lower

Question 17

Which of the following best describes a percentile?

Accepted Answer

The percentage of values in a dataset below a given value.

Question 18

If a boxplot for seniors has a longer whisker on the right than on the left, what does this indicate about the distribution of their SAT scores?

Accepted Answer

The distribution is skewed right.

Question 19

Which of the following is the correct formula for finding the percentile rank of a value $$x in a $$data set?

Accepted Answer

$$\frac{\# 	ext{ values below } x}{n} 	imes 100$$

Describing, Exploring, and Comparing Data: Measures of Center and Variation

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