Q: Which formula would you use to estimate the sample standard deviation using the range rule of thumb?

$$s \approx \frac{\text{range}}{4}$$

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

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

Q: A sample has a mean of 40 and a standard deviation of 8. What is the coefficient of variation (CV)? (Use the formula $$CV = \frac{s}{\bar{x}} \times 100)$$

$$CV = \frac{8}{40} \times 100 = 20\%$$

Question 1

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean is not resistant because a single extreme value can substantially change its value.

Question 2

Given the following sample data: 4, 7, 9, 10, 12, what is the mean? (Use the formula $$x = \Sigma x / n)$$

Accepted Answer

Mean = $$\frac{4+7+9+10+12}{5} = \frac{42}{5} = 8.4$$

Question 3

Which measure of center is most appropriate to use when a data set contains extreme outliers?

Accepted Answer

Median

Question 4

A data set has the following values: 2, 5, 7, 9, 12, 15. What is the midrange? (Use the formula $$	ext{Midrange} = \frac{	ext{max} + 	ext{min}}{2})$$

Accepted Answer

Midrange = $$\frac{15+2}{2} = \frac{17}{2} = 8.5$$

Question 5

Which of the following is NOT a property of the mode?

Accepted Answer

The mode is always the smallest value in the data set.

Question 6

A sample has the following values: 3, 7, 7, 8, 10. What is the mode?

Accepted Answer

Mode = 7

Question 7

Which formula would you use to estimate the sample standard deviation using the range rule of thumb?

Accepted Answer

$$s \approx \frac{	ext{range}}{4}$$

Question 8

A sample has a mean of 20 and a standard deviation of 4. According to the range rule of thumb, what values are considered significantly low and significantly high?

Accepted Answer

Significantly low: $$\leq 12$$; Significantly high: $$\geq 28$$

Question 9

Which statement about the standard deviation is FALSE?

Accepted Answer

The standard deviation is resistant to outliers.

Question 10

Given a sample with values: 5, 8, 12, 15, what is the range? (Use the formula $$	ext{Range} = 	ext{max} - 	ext{min})$$

Accepted Answer

Range = $$15 - 5 = 10$$

Question 11

A sample has a mean of 50 and a standard deviation of 5. What is the z score for a value of 60? (Use the formula $$z = \frac{x - \bar{x}}{s})$$

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 12

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 13

A sample has a mean of 40 and a standard deviation of 8. What is the coefficient of variation (CV)? (Use the formula $$CV = \frac{s}{\bar{x}} 	imes 100)$$

Accepted Answer

$$CV = \frac{8}{40} 	imes 100 = 20\%$$

Question 14

According to Chebyshev’s Theorem, what proportion of values must lie within 2 standard deviations of the mean for any data set?

Accepted Answer

At least $$1 - \frac{1}{2^2$} = 0.75 or 75$$%

Question 15

Which of the following is NOT part of the 5-number summary?

Accepted Answer

Mean

Question 16

A data set has $$Q_1 = 20$ and Q_3$ = 40. $$What is the interquartile range (IQR)? (Use the formula $$IQR = Q_3$ - Q_1$)

Accepted Answer

IQR = $$40 - 20 = 20$$

Question 17

If a sample has values: 2, 4, 6, 8, 10, what is the mean absolute deviation (MAD)? (Use the formula $$MAD = \frac{\Sigma |x - \bar{x}|}{n})$$

Accepted Answer

Mean = $$\frac{2+4+6+8+10}{5} = 6$$; MAD = $$\frac{|2-6|+|4-6|+|6-6|+|8-6|+|10-6|}{5} = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4$$

Question 18

Which of the following statements about variance is TRUE?

Accepted Answer

Variance is never negative and is zero only when all values are the same.

Measures of Center and Variation in Statistics: Study Notes

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