Q: A company tracks the annual returns of an investment: Year 1: -50%, Year 2: +100%. What is the geometric mean rate of return over the two years?

$\left[(1-0.5) \times (1+1.0)\right]^{1/2} - 1 = 0$

Q: A boxplot is constructed using which of the following summary statistics?

Minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum

Q: A data set has a mean of 100 and a standard deviation of 0. What can you conclude about the data?

All values in the data set are 100.

Q: Which formula is used to calculate the sample variance ($s^2$) for a data set of $n$ values?

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

Q: A business analyst wants to compare the variability of two investments: Investment A has a mean return of 8% and a standard deviation of 4%. Investment B has a mean return of 12% and a standard deviation of 6%. Which investment has a higher coefficient of variation?

Investment A: $CV = \frac{4\%}{8\%} \times 100\% = 50\%$

Question 1

Which of the following statements best describes the difference between the mean and the median as measures of central tendency?

Accepted Answer

The mean is more sensitive to extreme values (outliers) than the median.

Question 2

A real estate analyst is comparing home prices in two neighborhoods. Neighborhood A has a mean price of $300,000 and a standard deviation of $60,000. Neighborhood B has a mean price of $500,000 and a standard deviation of $50,000. Which neighborhood has greater relative variability in home prices?

Accepted Answer

Neighborhood A, because its coefficient of variation is higher.

Question 3

Given the following sample data: 8, 12, 15, 20, 25. What is the sample mean?

Accepted Answer

$\frac{8+12+15+20+25}{5} = 16$

Question 4

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is unaffected by extreme values (outliers).

Question 5

A company tracks the annual returns of an investment: Year 1: -50%, Year 2: +100%. What is the geometric mean rate of return over the two years?

Accepted Answer

$\left[(1-0.5) 	imes (1+1.0)ight]^{1/2} - 1 = 0$

Question 6

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile ($Q_3$) and the first quartile ($Q_1$).

Question 7

A sample of exam scores has a mean of 70 and a standard deviation of 10. What is the Z-score for a student who scored 85?

Accepted Answer

$z = \frac{85-70}{10} = 1.5$

Question 8

Which of the following statements about the coefficient of correlation ($r$) is TRUE?

Accepted Answer

It measures the strength and direction of a linear relationship between two variables.

Question 9

If a data set is right-skewed, which of the following is the most likely relationship among the mean, median, and mode?

Accepted Answer

Mode < Median < Mean

Question 10

A boxplot is constructed using which of the following summary statistics?

Accepted Answer

Minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum

Question 11

Suppose the mean SAT score is 500 with a standard deviation of 90. According to the empirical rule, approximately what percentage of students scored between 410 and 590?

Accepted Answer

68%

Question 12

Which of the following is a resistant measure of central tendency or variation?

Accepted Answer

Median

Question 13

A data set has a mean of 100 and a standard deviation of 0. What can you conclude about the data?

Accepted Answer

All values in the data set are 100.

Question 14

Which formula is used to calculate the sample variance ($s^2$) for a data set of $n$ values?

Accepted Answer

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

Question 15

A business analyst wants to compare the variability of two investments: Investment A has a mean return of 8% and a standard deviation of 4%. Investment B has a mean return of 12% and a standard deviation of 6%. Which investment has a higher coefficient of variation?

Accepted Answer

Investment A: $CV = \frac{4\%}{8\%} 	imes 100\% = 50\%$

Question 16

Which of the following statements about covariance is FALSE?

Accepted Answer

The magnitude of covariance can be used to compare the strength of relationships between different pairs of variables.

Question 17

If a data value has a Z-score of 3.5, what does this indicate?

Accepted Answer

The value is 3.5 standard deviations above the mean and is considered an extreme outlier.

Question 18

Which of the following best describes the purpose of a boxplot?

Accepted Answer

To display the distribution of a data set based on the five-number summary.

Question 19

According to Chebyshev’s Rule, at least what percentage of data values will fall within $k=2$ standard deviations of the mean, regardless of the data’s distribution?

Accepted Answer

75%

Question 20

Which of the following is NOT a recommended ethical practice when reporting numerical descriptive measures?

Accepted Answer

Reporting only the summary measures that support your argument.

Numerical Descriptive Measures in Business Statistics

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