Question 1

Which of the following best describes the shape of the distribution in the histogram of monthly average prices (see the green histogram with 'Monthly Average Price' on the x-axis)?

Accepted Answer

The distribution is unimodal and approximately symmetric.

Question 2

A histogram shows a distribution with two distinct peaks. What is the best term to describe this distribution?

Accepted Answer

Bimodal

Question 3

Which measure of center is most appropriate for a distribution that is highly skewed with several outliers?

Accepted Answer

Median

Question 4

Given a dataset with a mean of $$100,000 and a standard deviation of 20$$,000, what is the z-score for a value of $$140,000?

z$$ = \frac{x - \bar{x}}{s}$

Accepted Answer

$$z = 2$$

Question 5

Which of the following statements about the interquartile range (IQR) is TRUE?

Accepted Answer

The IQR measures the spread of the middle 50% of the data.

Question 6

A distribution is described as 'skewed to the right.' Which of the following is most likely TRUE?

Accepted Answer

The mean is greater than the median.

Question 7

If a dataset has a mean of 50 and a standard deviation of 5, what is the standardized value (z-score) for an observation of 40?

$$z = \frac{x - \bar{x}}{s}$$

Accepted Answer

$$z = -2$$

Question 8

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

Accepted Answer

Spread

Question 9

A real estate analyst finds that the average house price is $$175,000 with a standard deviation of 55$$,000. What is the z-score for a house priced at $$340,000?

z$$ = \frac{340,000 - 175,000}{55,000}$

Accepted Answer

$$z = 3$$

Question 10

Which of the following pairs of summary statistics should be reported together for a symmetric, unimodal distribution?

Accepted Answer

Mean and standard deviation

Question 11

Suppose you have a dataset with a minimum value of 10 and a maximum value of 90. What is the range?

Accepted Answer

Range = 80

Question 12

Which of the following is a reason to standardize variables using z-scores?

Accepted Answer

To compare values measured on different scales

Question 13

A histogram of hospital charges for cardiac patients is shown to be skewed to the right. Which measure of center and spread should be reported?

Accepted Answer

Median and IQR

Question 14

If a distribution is uniform, which of the following is TRUE?

Accepted Answer

All values occur with approximately the same frequency.

Question 15

Which of the following is the formula for the sample variance $$s^2$$?

Accepted Answer

$$s^2$$ = \frac{\sum (y - \bar{y}$$)^2$$}{n-1}$$

Question 16

Which of the following is NOT a possible reason for an outlier in a dataset?

Accepted Answer

A value that is typical for the dataset

Question 17

A dataset has $$Q_1 = 25$ and Q_3$ = 75. $$What is the interquartile range (IQR)?

$$IQR = Q_3$ - Q_1$

Accepted Answer

$$IQR = 50$$

Question 18

Which of the following best describes a histogram with all bars approximately the same height?

Accepted Answer

Uniform

Question 19

If a distribution has multiple modes, what should you consider doing when analyzing the data?

Accepted Answer

Try to determine if the data can be split into separate groups.

Question 20

Which of the following is TRUE about the standard deviation?

Accepted Answer

It is appropriate for symmetric distributions.

Displaying and Describing Quantitative Data: Study Notes for Business Statistics

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