Q: A law firm needs to compute the mean income for seven ski instructors, weighted by the number of days worked. Which formula should they use?

$$\text{Weighted Mean} = \frac{\sum w_i x_i}{\sum w_i}$$

Q: The 80th percentile of a data set with 30 values is located at which index position?

$$i = \frac{80}{100} \times 30 = 24$$

Q: The range of a data set is calculated as:

$$\text{Range} = \text{maximum value} - \text{minimum value}$$

Question 1

Which of the following statements best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is computed from the entire population and remains constant unless the population changes, while a statistic is computed from a sample and can vary depending on the sample selected.

Question 2

A sample of seven data analysts in Wisconsin had annual salaries of $$144,000, 98$$,000, $$204,000, 177$$,000, $$155,000, 316$$,000, and $100,000. What is the sample mean salary?

Accepted Answer

$$\170$$,571.43$

Question 3

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

Accepted Answer

Median

Question 4

Given the following sorted salaries: $$98,000; 100$$,000; $$144,000; 155$$,000; $$177,000; 204$$,000; $316,000, what is the median salary?

Accepted Answer

$$\155$$,000$

Question 5

If a data set is right-skewed, which of the following is true?

Accepted Answer

The mean is greater than the median.

Question 6

A frequency distribution of group sizes at a restaurant shows that the values 2 and 4 each occurred six times in a sample of 20 groups. What is the mode?

Accepted Answer

Both 2 and 4

Question 7

Which of the following statements about the mode is correct?

Accepted Answer

The mode is the value that occurs most frequently in the data.

Question 8

A law firm needs to compute the mean income for seven ski instructors, weighted by the number of days worked. Which formula should they use?

Accepted Answer

$$	ext{Weighted Mean} = \frac{\sum w_i x_i}{\sum w_i}$$

Question 9

The 80th percentile of a data set with 30 values is located at which index position?

Accepted Answer

$$i = \frac{80}{100} 	imes 30 = 24$$

Question 10

Which values are included in the five-number summary used for a box and whisker plot?

Accepted Answer

Minimum, first quartile, median, third quartile, maximum

Question 11

For a box and whisker plot, how are outliers identified?

Accepted Answer

Any value outside the limits $$Q_1 - 1.5$$($$Q_3$$ - $$Q_1$$)$$ and Q_3$ + 1.5(Q_3$ - Q_1$)$$

Question 12

The range of a data set is calculated as:

Accepted Answer

$$	ext{Range} = 	ext{maximum value} - 	ext{minimum value}$$

Question 13

Which measure of variation is less sensitive to extreme values than the range?

Accepted Answer

Interquartile range

Question 14

Given a sample of 100 text message counts with $$Q_1 = 178.0$ and Q_3$ = 220.5$$, what is the interquartile range?

Accepted Answer

$$42.5$$

Question 15

The population variance is calculated as:

Accepted Answer

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

Question 16

The sample standard deviation is calculated as:

Accepted Answer

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

Question 17

The coefficient of variation (CV) for a sample is calculated as:

Accepted Answer

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

Question 18

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

Accepted Answer

95%

Question 19

Tchebysheff’s theorem states that for any data distribution, at least what percentage of values fall within $$k = 2$$ standard deviations of the mean?

Accepted Answer

75%

Question 20

A standardized data value (z-score) for a population is calculated as:

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Describing Data Using Numerical Measures: Business Statistics Study Guide

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