Question 1

Suppose you have the following data set representing the travel times (in minutes) to work for seven employees: 23, 36, 23, 18, 5, 26, 43. What is the population mean travel time?

Accepted Answer

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

Question 2

Given the same data set: 23, 36, 23, 18, 5, 26, 43. What is the median travel time?

Accepted Answer

$$M = 23$$ minutes

Question 3

If a new employee with a travel time of 70 minutes is added to the previous data set, what is the new median?

Accepted Answer

$$M = \dfrac{23 + 26}{2} = 24.5$$ minutes

Question 4

Which measure of central tendency is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 5

A data set has the following values: 1, 2, 3, 6, 7, 8, 9, 10. What is the mode?

Accepted Answer

There is no mode

Question 6

What is the formula for the sample mean $$\overline{x}$$ given $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\overline{x} = \dfrac{\sum x_i}{n}$$

Question 7

Which of the following best describes when to use the mean as a measure of central tendency?

Accepted Answer

When the data are quantitative and the frequency distribution is roughly symmetric

Question 8

Given the data set: 23, 36, 23, 18, 5, 26, 43. What is the range?

Accepted Answer

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

Question 9

Which formula correctly represents the population standard deviation $$\sigma$$?

Accepted Answer

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

Question 10

If a data set is skewed right, which of the following is true about the mean and median?

Accepted Answer

Mean \u003e Median

Question 11

A sample of 4 values has a mean of 10. If three of the values are 8, 12, and 9, what is the fourth value?

Accepted Answer

11

Question 12

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

Accepted Answer

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

Question 13

A frequency distribution for hours spent studying per week is given. The midpoint of each class is multiplied by its frequency, and the sum is divided by the total frequency. What is being calculated?

Accepted Answer

The mean from grouped data

Question 14

Bob mixes 1 lb of raisins at $$1.25/lb, 2 lbs of chocolate peanuts at 3.25/lb$$, and 1.5 lbs of cashews at $5.40/lb. What is the weighted mean price per pound?

Accepted Answer

$$\dfrac{1(1.25) + 2(3.25) + 1.5(5.40)}{1 + 2 + 1.5} = 3.52$$

Question 15

Which of the following is the correct formula for a z-score for a population?

Accepted Answer

$$z = \dfrac{x - \mu}{\sigma}$$

Question 16

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

Accepted Answer

Approximately 95%

Question 17

Chebyshev’s Inequality states that for any data set, at least what percentage of observations lie within $$k = 3$$ standard deviations of the mean?

Accepted Answer

At least $$1 - \dfrac{1}{3^2$} = 1 - \dfrac{1}{9} = 0.8889 or 88.89$$%

Question 18

What is the interquartile range (IQR) for the data set: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40, if $$Q_1 = 28$ and Q_3$ = 38$$?

Accepted Answer

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

Question 19

Which of the following is NOT included in the five-number summary?

Accepted Answer

The mean

Chapter 3: Numerically Summarizing Data – Study Guide

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