Q: If 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 for the heights?

$$CV = \dfrac{3.3}{72.8} \times 100\% \approx 4.5\%$$

Q: A sample of 50 households has a mean number of children of 1.8 and a sample standard deviation of 1.7. What is the coefficient of variation?

$$CV = \dfrac{1.7}{1.8} \times 100\% \approx 94.4\%$$

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.

Question 2

Given the following salaries (in $$1000s): 41, 38, 39, 45, 47, 41, 44, 41, 37, 42, what is the population variance? Use $$\mu = 41.5$$ and N = 10$.

Accepted Answer

$$\$$sigma^2$$ = \dfrac{88.5}{10} = 8.85$$

Question 3

Which formula is used to calculate the sample standard deviation for grouped data?

Accepted Answer

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

Question 4

A data set has a mean of 50 and a standard deviation of 5. According to the Empirical Rule, approximately what percent of the data falls between 45 and 55?

Accepted Answer

68%

Question 5

Chebychev’s Theorem states that for any data set, at least what percent of the data lies within 2 standard deviations of the mean?

Accepted Answer

75%

Question 6

If 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 for the heights?

Accepted Answer

$$CV = \dfrac{3.3}{72.8} 	imes 100\% \approx 4.5\%$$

Question 7

Which of the following is NOT part of the five-number summary required for a box-and-whisker plot?

Accepted Answer

The mean

Question 8

A student scored 1600 on the SAT, which is at the 62nd percentile. What does this mean?

Accepted Answer

62% of students scored 1600 or less.

Question 9

Given a data set with $$Q_1 = 10$, Q_2$ = 18$$, and $$Q_3 = 31$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 31 - 10 = 21$$

Question 10

What is the z-score for a value $$x = 29 in a $$population with mean $$\mu = 49.5$$ and standard deviation $$\sigma = 13.8$$?

Accepted Answer

$$z = \dfrac{29 - 49.5}{13.8} \approx -1.49$$

Question 11

Which statement about standard deviation is TRUE?

Accepted Answer

A larger standard deviation indicates that data values are more spread out from the mean.

Question 12

If a data set is highly skewed, which measure is most affected?

Accepted Answer

The mean

Question 13

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

Accepted Answer

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

Question 14

A sample of 50 households has a mean number of children of 1.8 and a sample standard deviation of 1.7. What is the coefficient of variation?

Accepted Answer

$$CV = \dfrac{1.7}{1.8} 	imes 100\% \approx 94.4\%$$

Question 15

Which of the following best describes a percentile?

Accepted Answer

A value below which a given percentage of observations fall.

Question 16

If a value has a z-score of 2.5, how would you interpret this?

Accepted Answer

The value is 2.5 standard deviations above the mean and is considered unusual.

Question 17

Which of the following is true about the interquartile range (IQR)?

Accepted Answer

It measures the spread of the middle 50% of the data.

Question 18

A box-and-whisker plot is useful for:

Accepted Answer

Identifying outliers and visualizing the spread of a data set.

Question 19

Which of the following statements about Chebychev’s Theorem is correct?

Accepted Answer

It applies to any data set, regardless of distribution shape.

Descriptive Statistics: Measures of Variation and Position

Study Guide - Practice Questions

Study Guide - Flashcards