$$Q_3 + 1.5$$ \times IQR = 38 + 1.5 \times 10 = 53$$

Question 1

A start-up company has the following employee commute times (in minutes): 23, 36, 23, 18, 5, 26, 43. What is the population mean commute time?

Accepted Answer

$$\mu = \frac{23 + 36 + 23 + 18 + 5 + 26 + 43}{7} = 24.9$$ minutes

Question 2

Which of the following statements best describes a resistant statistic?

Accepted Answer

A statistic that is not affected substantially by extreme values in the data set.

Question 3

Given the data set: 5, 18, 23, 23, 26, 36, 43, what is the median?

Accepted Answer

$$M = 23$$

Question 4

If a new employee with a 130-minute commute joins the company, how does this affect the mean and median commute times?

Accepted Answer

The mean increases substantially, but the median increases only slightly.

Question 5

Which measure of central tendency is most appropriate for describing the most frequent observation in a data set?

Accepted Answer

Mode

Question 6

The range of the data set 23, 36, 23, 18, 5, 26, 43 is:

Accepted Answer

$$R = 43 - 5 = 38$$ minutes

Question 7

Which formula correctly represents the population standard deviation?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2$}{N}}$$

Question 8

A sample of three commute times is 5, 26, and 36 minutes. What is the sample standard deviation?

Accepted Answer

$$s = \sqrt{\frac{(5-22.33)^2$ + (26-22.33)^2$ + (36-22.33)^2$}{2}} \approx 15.82$$ minutes

Question 9

According to the Empirical Rule, what percentage of data in a bell-shaped distribution lies within two standard deviations of the mean?

Accepted Answer

Approximately 95%

Question 10

Using Chebyshev’s Inequality, what is the minimum percentage of data that must lie within $$k = 3$$ standard deviations of the mean for any data set?

Accepted Answer

At least $$1 - \frac{1}{3^2$} = 1 - \frac{1}{9} = \frac{8}{9} \approx 88.9\%$$

Question 11

A student’s z-score on an exam is $$z = 2.0. $$What does this mean?

Accepted Answer

The student’s score is 2 standard deviations above the mean.

Question 12

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

Accepted Answer

$$\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$$

Question 13

If the mean is greater than the median in a data set, what is the likely shape of the distribution?

Accepted Answer

Skewed right

Question 14

What is the interquartile range (IQR) for the data set with $$Q_1 = 28$ and Q_3$ = 38$$?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 38 - 28 = 10$$

Question 15

Which of the following is NOT part of the five-number summary?

Accepted Answer

The mean

Question 16

A boxplot shows a long whisker on the right side. What does this indicate about the data?

Accepted Answer

The data is skewed right.

Question 17

Given a data set with $$Q_1 = 28$, Q_3$ = 38$$, and $$IQR = 10$$, what is the upper fence for detecting outliers?

Accepted Answer

$$Q_3 + 1.5$$ 	imes IQR = 38 + 1.5 	imes 10 = 53$$

Question 18

Which of the following best describes the mode of a data set?

Accepted Answer

The value that occurs most frequently in the data set.

Chapter 3: Numerically Summarizing Data – Introductory Statistics Study Guide

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