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

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

Question 1

Which of the following best describes what the standard deviation measures in a data set?

Accepted Answer

The typical amount that values differ from the mean.

Question 2

Given the following recovery times (in days) for a sample of high school football players: 8, 10, 4, 6, 7, 7, 9, 10, 7, 6, 5, 11, what is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = 7.6$$

Question 3

If the mean starting salary for two corporations is $$51,500 and the range for Corporation A is 10$$,000 while for Corporation B it is $35,000, what does this indicate about the variation in salaries?

Accepted Answer

Corporation B has more variation in salaries.

Question 4

Which formula correctly represents the sample standard deviation $$s$$ for a data set with $$n$$ values and mean $$\bar{x}$$?

Accepted Answer

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

Question 5

A normal distribution has a mean of 100 and a standard deviation of 15. According to the Empirical Rule, approximately what percentage of data falls between 85 and 115?

Accepted Answer

68%

Question 6

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

Accepted Answer

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

Question 7

Why is the coefficient of variation (CV) useful when comparing the variability of two data sets with different units?

Accepted Answer

It removes the effect of units by expressing variation as a percentage of the mean.

Question 8

A sample of home prices is grouped into classes. To estimate the sample standard deviation for this grouped data, which value should be used for each class?

Accepted Answer

The midpoint of each class.

Question 9

If a data set is highly skewed, which measure of center and spread should be used to summarize the data?

Accepted Answer

Median and interquartile range (IQR).

Question 10

Suppose the mean height of a basketball team is 72.8 inches with a standard deviation of 3.3 inches. What is the coefficient of variation (CV) for the heights?

Accepted Answer

$$CV = 4.5\%$$

Question 11

A data set has a mean of 50 and a standard deviation of 5. According to Chebychev’s Theorem, at least what percentage of data falls within two standard deviations of the mean?

Accepted Answer

At least 75%

Question 12

Which of the following statements is TRUE about the range as a measure of variation?

Accepted Answer

The range is affected only by the two most extreme values.

Question 13

A hospital tracks the serum sodium (Na⁺) levels of patients. If the mean is 140 mmol/L and the standard deviation is 4 mmol/L, what is the 'usual range' for sodium levels?

Accepted Answer

$$132 to$$ $$148$$ mmol/L

Question 14

Which scenario best illustrates when the Empirical Rule can be applied?

Accepted Answer

A data set that is symmetric and unimodal.

Question 15

If the standard deviation of GPA scores is 0.7 and the standard deviation of annual incomes is $5,700, why can't you directly compare these values to determine which has more variation?

Accepted Answer

Because the units and scales are different.

Question 16

A sample of 20 families is surveyed about the number of children they have. The data is grouped into classes. Which step is necessary to estimate the sample mean and standard deviation?

Accepted Answer

Use the midpoint of each class and the class frequencies.

Question 17

Which of the following is NOT a reason to use the coefficient of variation (CV)?

Accepted Answer

To compare the central tendency of two data sets.

Question 18

If a data set has a mean of 100 and a standard deviation of 20, what is the value two standard deviations above the mean?

Accepted Answer

$$140$$

Question 19

Which of the following best describes the effect of outliers on the standard deviation?

Accepted Answer

Outliers increase the standard deviation.

Chapter 2.4: Measures of Variation – Descriptive Statistics Study Guide

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