Question 1

Which of the following best describes the mean in a symmetric distribution?

Accepted Answer

It is the balancing point of the distribution and represents a typical value.

Question 2

A sample of gas prices at 10 stations in Austin, Texas, is: $$3.19, 3.09$$, $$3.09, 2.93$$, $$2.95, 3.09$$, $$2.99, 2.99$$, $$2.95, 2.97. $$What is the formula for calculating the mean price $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{10} x_i}{10}$$

Question 3

In which scenario is the mean NOT a good representation of a typical value?

Accepted Answer

When the distribution is skewed.

Question 4

A city’s air quality is measured by the amount of particulate matter in micrograms per cubic meter. The mean is 7.9 and the standard deviation is 2.18. What is the range of values within one standard deviation of the mean?

Accepted Answer

$$5.72 to$$ $$10.08$$

Question 5

Which of the following statements about standard deviation is TRUE?

Accepted Answer

It is the square root of the variance.

Question 6

Given the following heights (in inches) for Team I: 72, 73, 76, 76, 78, and Team II: 67, 72, 76, 76, 84, which team has more variability in heights?

Accepted Answer

Team II, because its standard deviation is larger.

Question 7

Which formula correctly represents the sample variance $$s^2$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^n (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 8

A histogram of daily high temperatures in Provo, Utah, and San Francisco, CA, both show symmetric distributions, but Provo’s data is more spread out. What does this indicate?

Accepted Answer

Provo has a larger standard deviation.

Question 9

If a data set is roughly symmetric, which measure(s) should you use to describe its center and spread?

Accepted Answer

Mean and standard deviation

Question 10

A sample of tennis player winnings is highly skewed to the right. Which measure of center is most likely to be misleading?

Accepted Answer

The mean

Question 11

Suppose the mean price of gas is $$3.02 and the standard deviation is 0.09. $$What does the standard deviation tell you about the gas prices?

Accepted Answer

Most prices are within $$0.09 of 3.02.$$

Question 12

Which of the following is NOT a property of the mean?

Accepted Answer

It always represents the most frequent value.

Question 13

A data set has a mean of 50 and a standard deviation of 5. What is the value two standard deviations above the mean?

Accepted Answer

$$60$$

Question 14

Why is the standard deviation preferred over the variance when describing the spread of a data set?

Accepted Answer

Because it has the same units as the original data.

Question 15

Which of the following best describes what the standard deviation measures?

Accepted Answer

The typical distance of the observations from the mean.

Describing Data Numerically: The Mean and Standard Deviation

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