Q: Which formula would you use to calculate the coefficient of variation (CV) for a sample?

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

Question 1

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

Accepted Answer

It is a measure of how much the values in the data set typically deviate from the mean.

Question 2

Given the following recovery times (in days) for a sample of 12 athletes: 8, 10, 4, 6, 7, 7, 9, 10, 7, 6, 5, 11, what is the formula for the sample standard deviation $$s$$?

Accepted Answer

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

Question 3

A company has two departments. Both have the same mean salary, but Department A has a range of $$10,000 and Department B has a range of 35$$,000. What does this indicate about the salaries?

Accepted Answer

Department B has more variation in salaries.

Question 4

Which formula would you use to calculate the coefficient of variation (CV) for a sample?

Accepted Answer

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

Question 5

If a data set is symmetric and unimodal, which measures of center and spread are most appropriate to use?

Accepted Answer

Mean and standard deviation

Question 6

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 7

A researcher wants to compare the variability of heights (in inches) and weights (in pounds) of basketball players. Which statistic should they use?

Accepted Answer

Coefficient of variation (CV)

Question 8

Given a frequency distribution with classes, how do you estimate the sample mean and standard deviation?

Accepted Answer

Use the midpoint of each class for calculations.

Question 9

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 10

A sample of 20 families was surveyed about the number of children they have. The data is grouped into classes. Which method should be used to estimate the sample standard deviation?

Accepted Answer

Use the midpoints of the classes and the frequencies.

Question 11

Which of the following statements about the range is true?

Accepted Answer

The range is the difference between the highest and lowest values in a data set.

Question 12

If a data set is highly skewed, which measures of center and spread should be used to best describe the data?

Accepted Answer

Median and interquartile range (IQR)

Question 13

A serum sodium level is considered unusual if it falls outside the usual range. If the mean is 140 mmol/L and the standard deviation is 4 mmol/L, what is the usual range?

Accepted Answer

$$140 \pm 2 	imes 4$$

Question 14

Which of the following is NOT a correct interpretation of the standard deviation?

Accepted Answer

It measures the center of the data.

Question 15

Using the Empirical Rule, what percentage of data falls within three standard deviations of the mean in a normal distribution?

Accepted Answer

99.7%

Question 16

A data set has a mean of 50 and a standard deviation of 5. According to the Empirical Rule, what is the range that contains approximately 68% of the data?

Accepted Answer

$$50 \pm 1 	imes 5$$

Question 17

Which of the following is a correct formula for the population variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum (x_i - \mu)^2$}{N}$$

Question 18

A city’s home prices are grouped into classes. To estimate the sample mean and standard deviation, which value should be used for each class?

Accepted Answer

The class midpoint

Question 19

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 different units by expressing variation as a percentage of the mean.

Descriptive Statistics: Measures of Variation

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