Question 1

A researcher collects the following data on the number of homes foreclosed in seven states: 173,175; 49,723; 20,352; 10,824; 40,911; 18,038; 61,848. What is the median number of homes foreclosed?

Accepted Answer

$$40,911$$

Question 2

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

Accepted Answer

Mean

Question 3

Given the following cash donations (in millions) by eight U.S. companies: 319, 199, 110, 63, 21, 315, 26, 63. What is the mean donation?

Accepted Answer

$$139.5$$

Question 4

A data set has the following values: 21, 19, 27, 22, 29, 19, 25, 21, 22, 30. What is the mode of this data set?

Accepted Answer

19, 21, and 22

Question 5

Which of the following statements is TRUE about the relationship among mean, median, and mode in a distribution skewed to the right?

Accepted Answer

Mode \u003c Median \u003c Mean

Question 6

The range of the total area (in square miles) for Arkansas (53,182), Louisiana (49,651), Oklahoma (69,903), and Texas (267,277) is:

Accepted Answer

$$217,626$$

Question 7

Which formula correctly represents the sample variance for ungrouped data?

Accepted Answer

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

Question 8

A sample of 5000 people has a bell-shaped age distribution with mean $$40$$ years and standard deviation $$12$$ years. According to the Empirical Rule, approximately what percentage of people are between $$16$$ and $$64$$ years old?

Accepted Answer

$$95\%$$

Question 9

For the grouped data below, what is the mean daily commuting time?

| Daily Commuting Time (min) | Number of Employees |
|---------------------------|---------------------|
| 0 to \u003c10                  | 4                   |
| 10 to \u003c20                 | 9                   |
| 20 to \u003c30                 | 6                   |
| 30 to \u003c40                 | 4                   |
| 40 to \u003c50                 | 2                   |

Accepted Answer

$$21.40$$ minutes

Question 10

Which of the following is a disadvantage of using the range as a measure of dispersion?

Accepted Answer

It is based only on the largest and smallest values

Question 11

A company’s CEO compensation data (in millions) is: 21.6, 21.7, 22.9, 25.2, 26.5, 28.0, 28.2, 32.6, 32.9, 70.1, 76.1, 84.5. What is the interquartile range (IQR)?

Accepted Answer

$$27.45$$

Question 12

Which of the following best describes the Empirical Rule for a bell-shaped distribution?

Accepted Answer

Approximately $$68\% of $$values lie within one standard deviation, $$95\%$$ within two, and $$99.7\%$$ within three

Question 13

If a data set is skewed to the left, which of the following is the correct order of mean, median, and mode?

Accepted Answer

Mode \u003e Median \u003e Mean

Question 14

A sample of six U.S. airlines had baggage fee revenues (in millions): 313, 342, 581, 952, 514, 152. Given $$\sum x = 2854$$ and $$\sum x^2$ = 1,746,098$$, what is the sample variance?

Accepted Answer

$$s^2$$ = \frac{1,746,098 - $$(2854^2/6$$)}{5}$$

Question 15

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

Accepted Answer

It is always less than the mean

Question 16

According to Chebyshev’s theorem, at least what percentage of values lie within $$k = 3$$ standard deviations of the mean for any data set?

Accepted Answer

$$89\%$$

Question 17

Which measure of central tendency can be used for both quantitative and qualitative data?

Accepted Answer

Mode

Question 18

A box-and-whisker plot is constructed using which of the following values?

Accepted Answer

Median, first quartile, third quartile, smallest and largest values within inner fences

Chapter 3: Numerical Descriptive Measures in Introductory Statistics

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