Question 1

A business analyst is comparing the annual salaries of employees at two different companies. Company A's salaries are roughly symmetric with no outliers, while Company B's salaries are highly skewed to the right with several high outliers. Which measures of center and spread should the analyst use for each company?

Accepted Answer

For Company A, use the mean and standard deviation; for Company B, use the median and interquartile range (IQR).

Question 2

Which of the following best describes a histogram?

Accepted Answer

A graphical representation that displays the frequency of quantitative data divided into intervals (bins), with the height of each bar representing the number of observations in each bin.

Question 3

A dataset of monthly sales figures is summarized in a histogram with two distinct peaks. How should the shape of this distribution be described?

Accepted Answer

Bimodal

Question 4

Which of the following statements about the mean and median is TRUE?

Accepted Answer

The median is resistant to outliers, while the mean is not.

Question 5

A real estate agent wants to compare the price of a house to the average price in its neighborhood. The house is priced at $$500,000, the neighborhood mean is 400$$,000, and the standard deviation is $50,000. What is the z-score for this house price?

Accepted Answer

$$z = \frac{500,000 - 400,000}{50,000} = 2$$

Question 6

Which of the following is NOT a correct description of the interquartile range (IQR)?

Accepted Answer

The IQR is more affected by outliers than the range.

Question 7

A company tracks the number of products sold each day for a month. The histogram of sales per day is approximately uniform. What does this indicate about the distribution?

Accepted Answer

All sales values occur with roughly the same frequency; there is no clear mode.

Question 8

Which of the following is the correct formula for the z-score of a value $$x in a $$dataset with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 9

A dataset of delivery times has a mean of 30 minutes and a standard deviation of 5 minutes. A delivery took 45 minutes. What is the z-score for this delivery time?

Accepted Answer

$$z = \frac{45 - 30}{5} = 3$$

Question 10

Which of the following statements about outliers is correct?

Accepted Answer

Outliers can significantly affect the mean and standard deviation.

Question 11

A histogram of exam scores is skewed to the left. Which of the following is most likely true?

Accepted Answer

The mean is less than the median.

Question 12

A company wants to compare the variability of two different product lines. Product Line A has a standard deviation of 10 units, and Product Line B has a standard deviation of 20 units. What does this indicate?

Accepted Answer

Product Line B's sales are more spread out from the mean than Product Line A's.

Question 13

Which of the following best describes a relative frequency histogram?

Accepted Answer

A histogram where the y-axis shows the percentage of observations in each bin.

Question 14

A dataset of daily website visits has a mean of 1,000 and a standard deviation of 100. On a particular day, the website receives 1,300 visits. How unusual is this value?

Accepted Answer

It is 3 standard deviations above the mean, which is considered very unusual.

Question 15

A manager is analyzing the distribution of customer wait times and finds that the data is symmetric with no outliers. Which summary statistics should the manager report?

Accepted Answer

Mean and standard deviation

Question 16

Which of the following is the correct formula for the range of a dataset?

Accepted Answer

$$	ext{Range} = 	ext{Maximum} - 	ext{Minimum}$$

Question 17

A dataset of monthly electricity usage is multimodal. What does this suggest about the data?

Accepted Answer

There are three or more peaks, possibly indicating different groups or patterns in the data.

Question 18

If a value has a z-score of $$-2.5$$, what does this indicate?

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 19

A company is comparing the z-scores of two employees' sales numbers: Employee A has a z-score of 1.2, and Employee B has a z-score of 2.0. What can be concluded?

Accepted Answer

Employee B's sales are more unusual (further above the mean) than Employee A's.

Question 20

Which of the following pairs of summary statistics is most appropriate for describing a highly skewed distribution with outliers?

Accepted Answer

Median and interquartile range (IQR)

Displaying and Describing Quantitative Data: Study Notes for Business Statistics

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