Question 1

Which of the following statements best describes the median of a data set?

Accepted Answer

The median is the 50th percentile of the data.

Question 2

Given the following data set of trip durations (in seconds): 355, 884, 229, 417, 383. What is the sample mean?

Accepted Answer

$$\frac{355+884+229+417+383}{5} = 453.6$$

Question 3

A sample consists of the following savings (in thousands of dollars): 2, 10, 8, 7, 14. What is the median?

Accepted Answer

$$8$$

Question 4

If a data set is skewed right, which measure of center is generally a better representation of a typical value?

Accepted Answer

The median

Question 5

Suppose the savings data for five adults is: 2, 10, 8, 7, 14. If the person with $$14$$ thousand wins the lottery and now has $$914$$ thousand, what is the new mean savings?

Accepted Answer

$$\frac{2+10+8+7+914}{5} = 188.2$$

Question 6

Which of the following is true about the effect of an outlier on the mean and median?

Accepted Answer

An outlier affects the mean much more than the median.

Question 7

Given the following minimum wages for Pacific states: 9.89, 10.10, 11.25, 12.00, 12.00. What is the median?

Accepted Answer

$$11.25$$

Question 8

Given the following minimum wages for Mountain states: 5.15, 7.25, 7.25, 7.50, 8.25, 8.50, 11.00, 11.10. What is the median?

Accepted Answer

$$\frac{7.50+8.25}{2} = 7.875$$

Question 9

If a distribution is symmetric and unimodal, which measure of center is most appropriate?

Accepted Answer

The mean

Question 10

Which formula correctly represents the sample mean for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum x_i}{n}$$

Question 11

Which formula correctly represents the population mean for $$N$$ observations $$x_1$$, $$x_2$$, ..., x_N$$?

Accepted Answer

$$\mu = \frac{\sum x_i}{N}$$

Question 12

A data set consists of the following values: 1, 2, 2, 3, 4. What is the mode?

Accepted Answer

2

Question 13

Which of the following best describes a bimodal distribution?

Accepted Answer

A distribution with two distinct peaks or mounds.

Question 14

In a bimodal distribution of the number of days served by U.S. presidents, the mean is approximately 1907.6 days and the median is 1461 days. What does this indicate about the distribution?

Accepted Answer

The mean lies between the two mounds and does not represent a typical value.

Question 15

Which of the following is true about the mode of a data set?

Accepted Answer

There can be more than one mode if multiple values have the highest frequency.

Question 16

If all observations in a data set have frequency 1, what is the mode?

Accepted Answer

There is no mode.

Question 17

Which of the following best describes the relationship between the mean and median in a left-skewed distribution?

Accepted Answer

The mean is less than the median.

Question 18

Suppose you have the following data: 0, 0, 0, 1, 4, 0, 0, 0, 0, 0. What is the mode?

Accepted Answer

0

Question 19

Which of the following is the correct interpretation of $$\sum x_i in $$statistics?

Accepted Answer

The sum of all data values in the set.

Question 20

A researcher wants to compare the centers of two groups: one group is skewed left and the other is symmetric. Which measure of center should be used for each group?

Accepted Answer

Median for the skewed group, mean for the symmetric group.

Chapter 4: Summarizing Data Numerically – Measures of Center

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