Q: Which investment is riskier based on the coefficient of variation: Investment A with mean return $10$ and standard deviation $5$, or Investment B with mean return $20$ and standard deviation $8$?

Investment A: $CV = \frac{5}{10} \times 100 = 50\%$; Investment B: $CV = \frac{8}{20} \times 100 = 40\%$. Investment A is riskier.

Q: If the sample mean is $\overline{x} = 50$ and the sample standard deviation is $s = 10$, what is the coefficient of variation?

$CV = \frac{10}{50} \times 100 = 20\%$

Question 1

Which of the following is the correct formula for the sample variance?

Accepted Answer

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

Question 2

A company wants to summarize the distribution of employee salaries, which is highly skewed. Which summary statistics should they use?

Accepted Answer

Median and interquartile range (IQR)

Question 3

What does the coefficient of variation (CV) measure?

Accepted Answer

The standard deviation as a percentage of the mean

Question 4

Given the following data set: 2, 4, 7, 10, 15. What is the range?

Accepted Answer

$15 - 2 = 13$

Question 5

Which of the following statements about boxplots is TRUE?

Accepted Answer

Boxplots display the median, quartiles, and potential outliers of a data set.

Question 6

If a data set is symmetric, which measures should be used to summarize its central tendency and dispersion?

Accepted Answer

Mean and standard deviation

Question 7

A researcher finds that the 75th percentile of test scores is 88. What does this mean?

Accepted Answer

75% of the test scores are less than or equal to 88

Question 8

Which investment is riskier based on the coefficient of variation: Investment A with mean return $10$ and standard deviation $5$, or Investment B with mean return $20$ and standard deviation $8$?

Accepted Answer

Investment A: $CV = \frac{5}{10} 	imes 100 = 50\%$; Investment B: $CV = \frac{8}{20} 	imes 100 = 40\%$. Investment A is riskier.

Question 9

Which of the following is NOT a measure of variation?

Accepted Answer

Median

Question 10

A boxplot of systolic blood pressure for 200 adults shows a median of 133, $Q_1 = 119$, $Q_3 = 146.5$, min = 93.5, and max = 217. What is the interquartile range (IQR)?

Accepted Answer

$IQR = Q_3 - Q_1 = 146.5 - 119 = 27.5$

Question 11

Which scenario best illustrates the use of boxplots for decision-making in a technology company?

Accepted Answer

Comparing network latency distributions of two products to determine which is faster and more consistent.

Question 12

If the sample mean is $\overline{x} = 50$ and the sample standard deviation is $s = 10$, what is the coefficient of variation?

Accepted Answer

$CV = \frac{10}{50} 	imes 100 = 20\%$

Question 13

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

Accepted Answer

The range of the middle 50% of the data

Question 14

Why are mean and standard deviation not appropriate for summarizing highly skewed data?

Accepted Answer

They are sensitive to extreme values and outliers.

Question 15

A data set has $Q_1 = 20$, $Q_3 = 40$. What is the IQR and what does it represent?

Accepted Answer

$IQR = 20$; it represents the spread of the middle 50% of the data.

Question 16

Which of the following is a real-world example where percentiles are commonly used?

Accepted Answer

Reporting baby weights in growth charts

Question 17

If the minimum value in a data set is 5 and the maximum value is 25, what is the range?

Accepted Answer

$25 - 5 = 20$

Question 18

Which of the following is TRUE about outliers in a boxplot?

Accepted Answer

They are displayed as individual points outside the whiskers.

Question 19

A sample of restaurant ratings (out of 30) is symmetric with mean 21.27 and standard deviation 2.39. Which summary statistics are most appropriate?

Accepted Answer

Mean and standard deviation

Descriptive Statistics 2: Measures of Variation and Boxplots

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