Question 1

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

Accepted Answer

The balancing point of the distribution, calculated as the arithmetic average of all values.

Question 2

Suppose the distribution of ACT scores for a group of students is symmetric. Which measure of center is most appropriate to describe a typical score?

Accepted Answer

The mean

Question 3

A sample of gas prices at 10 stations is: $$3.19, 3.09$$, $$3.09, 2.93$$, $$2.95, 3.09$$, $$2.99, 2.99$$, $$2.95, 2.97. $$What is the mean price?

Use the formula: 
$$ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i $$

Accepted Answer

$3.02

Question 4

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean is a good estimate of a typical value when the distribution is roughly symmetric.

Question 5

A histogram of professional tennis players' winnings in 2020 is highly skewed to the right. Which measure of center would best represent a typical player's winnings?

Accepted Answer

The median

Question 6

What does the standard deviation measure in a data set?

Accepted Answer

The typical distance of the observations from the mean.

Question 7

Given a sample with mean $$\bar{x} = 7.9$$ and standard deviation $$s = 2.18$$, what is the value one standard deviation above the mean?

Accepted Answer

$$10.08$$

Question 8

If most of the data in a distribution is within one standard deviation of the mean, what does this suggest about the spread of the data?

Accepted Answer

The data is tightly clustered around the mean.

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

The standard deviation has the same units as the original data.

Question 11

A sample of five basketball players on Team I has heights (in inches): 72, 73, 76, 76, 78. The mean height is 75. What does a standard deviation of about 2.4 inches mean in this context?

Accepted Answer

On average, the players' heights differ from the mean by about 2.4 inches.

Question 12

Which scenario best illustrates when the mean is NOT a good measure of center?

Accepted Answer

A distribution of home prices with a few extremely expensive homes.

Question 13

If the standard deviation of gas prices at 10 stations is $0.09, what does this tell you about the prices?

Accepted Answer

Most prices are within 9 cents of the mean price.

Question 14

Which of the following is NOT a characteristic used to describe a numerical distribution?

Accepted Answer

Color

Question 15

A city’s air quality is measured by the amount of particulate matter in micrograms per cubic meter. If the mean is 7.9 and the standard deviation is 2.18, what is the range of values that includes most cities’ air quality?

Accepted Answer

Between 5.7 and 10.1

Question 16

Which of the following best explains why technology is often used to calculate the mean and standard deviation for large data sets?

Accepted Answer

Technology can quickly and accurately perform calculations that would be tedious and error-prone by hand.

Question 17

Which of the following is the correct interpretation of the mean in a symmetric distribution?

Accepted Answer

It is the balancing point and a good representation of a typical value.

Question 18

If a distribution is symmetric and has a small standard deviation, what can you conclude about the data?

Accepted Answer

Most data values are close to the mean.

Describing Data Numerically: Mean and Standard Deviation

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