Question 1

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

Accepted Answer

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

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 ages of students in a college class: 26, 33, 31, 23, 20, 19, 21, 18, 25. What is the median age?

Accepted Answer

23

Question 4

Which of the following statements about the mean and median is TRUE?

Accepted Answer

The mean is not resistant to outliers, while the median is resistant.

Question 5

A stemplot of pets owned by students is shown. Which is the mode of the data?

Accepted Answer

0

Question 6

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

Accepted Answer

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

Question 7

A sample of 500 random adult books in a library has an average of 312 pages with 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 8

The mean weight of milk bottles at a company is 12 oz and the standard deviation is 0.5 oz. According to the Empirical Rule, what is the range that contains approximately 95% of the bottles?

Accepted Answer

$$[11, 13]$$

Question 9

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 percentage of wait times are between 5.5 and 10.5 minutes?

Accepted Answer

68%

Question 10

A student collects data on the number of songs in playlists: 10, 11, 12, 10, 15, 12, 17, 20, 21, 11, 10, 11, 13, 24, 16, 12, 14, 15, 19, 18, 21, 12, 11, 10, 19, 20, 9, 16. What is the mode of this data?

Accepted Answer

10

Question 11

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

Accepted Answer

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

Question 12

A boxplot displays which of the following summaries?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 13

If a data set is symmetric and has no outliers, which measure of center is generally preferred?

Accepted Answer

Mean

Question 14

A student wants to estimate the standard deviation of song lengths, which range from 2.3 to 4.7 minutes. Using the range rule of thumb, what is the estimated standard deviation?

Accepted Answer

$$\dfrac{4.7 - 2.3}{4} = 0.6$$

Question 15

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It can be negative.

Question 16

Given the following boxplots for SAT scores of juniors and seniors, which class has a greater range of SAT scores?

Accepted Answer

Seniors

Question 17

Which of the following best describes a bimodal data set?

Accepted Answer

A data set with two modes

Question 18

If a value is at the 75th percentile in a data set, what does this mean?

Accepted Answer

75% of the data values are less than or equal to this value.

Question 19

Which scenario would most likely require the use of the median instead of the mean as a measure of center?

Accepted Answer

A data set of annual incomes in a city with a few extremely high earners.

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

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