Q: A dataset of monthly sales has a minimum value of 120 and a maximum value of 480. What is the range of the data?

$$\text{Range} = 480 - 120 = 360$$

Q: A dataset has a lower quartile (Q1) of 20 and an upper quartile (Q3) of 50. What is the interquartile range (IQR)?

$$\text{IQR} = Q3 - Q1 = 50 - 20 = 30$$

Question 1

A business analyst is comparing the annual salaries of employees in two departments. Department A has a symmetric distribution with no outliers, while Department B is highly skewed with several outliers. Which measures of center and spread should the analyst use for each department?

Accepted Answer

For Department A, use the mean and standard deviation; for Department B, use the median and IQR.

Question 2

Which of the following best describes a histogram?

Accepted Answer

A graphical representation of the distribution of a quantitative variable, dividing the data into bins and showing the frequency of observations in each bin.

Question 3

A company tracks the number of sales per day for a month. The histogram of sales per day shows two distinct peaks. How should the shape of this distribution be described?

Accepted Answer

Bimodal

Question 4

Which measure of center is resistant to outliers and skewed data?

Accepted Answer

Median

Question 5

A real estate agent wants to compare the price of a house to the average price in the neighborhood. The house costs $$350,000, the neighborhood mean is 300$$,000, and the standard deviation is $25,000. What is the z-score for the house price?

Accepted Answer

$$z = \frac{350,000 - 300,000}{25,000} = 2$$

Question 6

Which of the following statements about standard deviation is correct?

Accepted Answer

Standard deviation measures the average distance of data values from the mean and is appropriate for symmetric distributions without outliers.

Question 7

A dataset of monthly sales has a minimum value of 120 and a maximum value of 480. What is the range of the data?

Accepted Answer

$$	ext{Range} = 480 - 120 = 360$$

Question 8

A distribution of customer wait times is described as right-skewed. Which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 9

A manager wants to compare the performance of two employees using z-scores. Employee A has a z-score of 1.5 for sales, and Employee B has a z-score of -0.5. What does this indicate?

Accepted Answer

Employee A's sales are 1.5 standard deviations above the mean, Employee B's sales are 0.5 standard deviations below the mean.

Question 10

Which of the following best describes a uniform distribution in a histogram?

Accepted Answer

All bars are approximately the same height, with no clear mode.

Question 11

A dataset has a lower quartile (Q1) of 20 and an upper quartile (Q3) of 50. What is the interquartile range (IQR)?

Accepted Answer

$$	ext{IQR} = Q3 - Q1 = 50 - 20 = 30$$

Question 12

Which of the following is NOT a reason to report outliers in a dataset?

Accepted Answer

Outliers help determine the shape of the distribution.

Question 13

A histogram of daily website visits shows a long tail to the left. How should this distribution be described?

Accepted Answer

Left-skewed

Question 14

A company wants to compare the percentage of defective products in two factories with different production volumes. Which visualization tool should they use?

Accepted Answer

Relative frequency histogram

Question 15

If a dataset is symmetric and has no outliers, which pair of summary statistics should be used?

Accepted Answer

Mean and standard deviation

Question 16

A student scores 85 on a test where the mean is 80 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 80}{5} = 1$$

Question 17

Which of the following statements is true about the mean and median in a symmetric distribution?

Accepted Answer

The mean and median are equal.

Question 18

A dataset of monthly profits has the following values: $$10,000, 12$$,000, $$13,000, 15$$,000, $100,000. Which value is most likely an outlier?

Accepted Answer

$$100,000$$

Question 19

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

Accepted Answer

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

Displaying and Describing Quantitative Data: Study Notes for Business Statistics

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