Question 1

A sample of home prices (in thousands of dollars) is: 275, 229, 850, 240, 305, 287, 310, 342. Which measure of center is more representative of the data: mean or median? Why?

Accepted Answer

The median, because it is resistant to extreme values like 850.

Question 2

Given the data set $$\{5, 10, 14, 12, 3\}$$, what is the mean?

Accepted Answer

$$\displaystyle \frac{44}{5} = 8.8$$

Question 3

Which formula correctly calculates the sample mean $$\overline{x}$$?

Accepted Answer

$$\displaystyle \overline{x} = \frac{\sum x}{n}$$

Question 4

A sample of ages is: 24, 27, 30, 23, 20, 19, 21, 25, 18. What is the median?

Accepted Answer

24

Question 5

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

Accepted Answer

The median is not affected by extreme values.

Question 6

Given the data set $$\{5, 10, 14, 12, 3, 76\}$$, how does the outlier (76) affect the mean?

Accepted Answer

It increases the mean significantly.

Question 7

Which formula is used to calculate the sample standard deviation $$s$$?

Accepted Answer

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

Question 8

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

Accepted Answer

68%

Question 9

The wait times at a restaurant are normally distributed with 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 wait times?

Accepted Answer

3 to 13 minutes

Question 10

A data set of exam scores is: 55, 60, 65, 70, 75, 80, 85, 90, 95. What is the interquartile range (IQR)?

Accepted Answer

20

Question 11

Which of the following best describes the mode?

Accepted Answer

The value that occurs most frequently in a data set.

Question 12

A sample of playlist song counts is: 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?

Accepted Answer

10

Question 13

If a value is more than two standard deviations above the mean, how is it classified according to the Range Rule of Thumb?

Accepted Answer

Significantly high

Question 14

The 1st quartile (Q1) and 3rd quartile (Q3) of a data set are 20 and 40, respectively. What is the interquartile range (IQR)?

Accepted Answer

20

Question 15

A boxplot displays which of the following?

Accepted Answer

The five-number summary (minimum, Q1, median, Q3, maximum)

Question 16

A data set is symmetric and has no outliers. Which measure of center is most appropriate to use?

Accepted Answer

Mean

Question 17

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

Accepted Answer

It can be negative.

Question 18

A student finds that the range of song lengths is 2.4 minutes (from 2.3 to 4.7 minutes). Using the Range Rule of Thumb, estimate the standard deviation.

Accepted Answer

$$\displaystyle \frac{2.4}{4} = 0.6$$ minutes

Question 19

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.

Describing, Exploring, and Comparing Data (Ch. 3) – Measures of Center and Variation

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