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

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

Q: If the mean height of a group is 64.1 inches with a standard deviation of 2.6 inches, what is the height that is two standard deviations below the mean?

$$64.1 - 2 \times 2.6 = 58.9$$ inches

Question 1

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

Accepted Answer

The difference between the maximum and minimum data entries in the set.

Question 2

A sample of recovery times (in days) for 12 athletes after a concussion is: 8, 10, 4, 6, 7, 7, 9, 10, 7, 6, 5, 11. What is the formula for the sample variance $$s^2$$?

Accepted Answer

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

Question 3

Which statement about standard deviation is TRUE?

Accepted Answer

The standard deviation is always greater than or equal to 0.

Question 4

A population has the following data: 2, 4, 6, 8. What is the population mean $$\mu$$?

Accepted Answer

$$\mu = 5$$

Question 5

If a data set has a mean of 50 and a standard deviation of 5, what percentage of data falls within the range 45 to 55, assuming a bell-shaped distribution?

Accepted Answer

About 68%

Question 6

According to Chebychev’s Theorem, at least what percentage of data values must lie within 3 standard deviations of the mean for any data set?

Accepted Answer

About 88.9%

Question 7

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

Accepted Answer

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

Question 8

A data set has all entries equal to 7. What is the standard deviation?

Accepted Answer

0

Question 9

A sample of home prices in a city is grouped into classes. To estimate the sample mean and standard deviation, which value should be used for each class?

Accepted Answer

The midpoint of each class

Question 10

If the mean height of a group is 64.1 inches with a standard deviation of 2.6 inches, what is the height that is two standard deviations below the mean?

Accepted Answer

$$64.1 - 2 	imes 2.6 = 58.9$$ inches

Question 11

Which of the following is NOT a correct interpretation of the Empirical Rule for a bell-shaped distribution?

Accepted Answer

About 75% of data lie within one standard deviation of the mean.

Question 12

A researcher finds that the coefficient of variation for heights is 4.5% and for weights is 9.4% in a basketball team. What does this indicate?

Accepted Answer

Weights are more variable than heights.

Question 13

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

Accepted Answer

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

Question 14

A data set has a mean of 100 and a standard deviation of 15. According to Chebychev’s Theorem, at least what percentage of data values lie between 70 and 130?

Accepted Answer

At least 75%

Question 15

Which scenario best illustrates the use of the range as a measure of variation?

Accepted Answer

Comparing the highest and lowest starting salaries among new graduates at two companies.

Question 16

If a data set is highly spread out, what can you say about its standard deviation?

Accepted Answer

The standard deviation will be large.

Question 17

A sample of 50 households is grouped by number of children. To estimate the sample standard deviation, which formula should be used for grouped data?

Accepted Answer

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

Measures of Variation in Descriptive Statistics

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