Q: Which of the following is the correct formula for the coefficient of variation (CV) for a sample?

$$CV = \frac{s}{\overline{x}} \times 100\%$$

Question 1

Which of the following best describes the primary purpose of descriptive statistics in business?

Accepted Answer

To summarize and present data in a meaningful way.

Question 2

A company wants to understand the distribution of salaries among its employees. Which graphical technique would be most appropriate?

Accepted Answer

Histogram

Question 3

Given the following data set representing the number of products sold per day: 10, 12, 12, 15, 18, 20, 22. What is the median?

Accepted Answer

$$15$$

Question 4

Which measure is most affected by extreme values in a data set?

Accepted Answer

Mean

Question 5

A business analyst calculates the coefficient of variation for two different investments. Investment A has a mean return of $$8\%$$ and a standard deviation of $$2\%. $$Investment B has a mean return of $$12\%$$ and a standard deviation of $$3\%. $$Which investment is relatively more risky?

Accepted Answer

Investment A, because its coefficient of variation is higher.

Question 6

Which of the following formulas correctly represents the sample variance $$s^2$$ for a data set with $$n$$ observations and sample mean $$\overline{x}$$?

Accepted Answer

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

Question 7

A company tracks the number of customer complaints per month. Which type of data is this?

Accepted Answer

Discrete

Question 8

If a data set is highly skewed to the right, which of the following is most likely true?

Accepted Answer

Mode \u003c Median \u003c Mean

Question 9

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

Accepted Answer

The difference between the highest and lowest values.

Question 10

A business wants to compare the variability of sales between two regions. Region X has a standard deviation of $$500$$ units and a mean of $$2,000$$ units. Region Y has a standard deviation of $$300$$ units and a mean of $$1,000$$ units. Which region has greater relative variability?

Accepted Answer

Region Y, because its coefficient of variation is higher.

Question 11

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 12

A grouped data frequency distribution is most useful when:

Accepted Answer

The data set contains a large number of values.

Question 13

Which of the following statements about the standard deviation is TRUE?

Accepted Answer

It is measured in the same units as the data.

Question 14

A box and whisker plot is useful for:

Accepted Answer

Showing the distribution, median, and spread of a data set.

Question 15

Which of the following is the correct formula for the coefficient of variation (CV) for a sample?

Accepted Answer

$$CV = \frac{s}{\overline{x}} 	imes 100\%$$

Question 16

Which of the following best describes a parameter in statistics?

Accepted Answer

A numerical summary of a population.

Question 17

A company wants to estimate the average time customers spend on their website. Which sampling method would best ensure that all types of customers are represented?

Accepted Answer

Stratified sampling

Question 18

Which of the following is an example of inferential statistics?

Accepted Answer

Estimating the average income of all customers based on a sample.

Question 19

If the mean of a data set is $$50$$ and the standard deviation is $$5$$, what is the z-score for a value of $$60$$?

Accepted Answer

$$z = 2$$

Question 20

Which of the following best describes the purpose of data visualization in business statistics?

Accepted Answer

To summarize and communicate patterns in data effectively.

Study Guide: Data Collection, Visualization, and Description in Business Statistics

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