Question 1

Which of the following statements best describes the range as a measure of variability in a data set?

Accepted Answer

The range is the difference between the largest and smallest measurements in a data set.

Question 2

Given the following data set: 10, 15, 20, 25, 30. What is the sample variance? Use the formula $$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$.

Accepted Answer

$$s^2 = 62.5$

Question 3

A company’s profit margins for 100 jobs are shown in two histograms for two cost estimators. Estimator A’s histogram is more spread out than Estimator B’s. What can you infer about the variability of their profit margins?

Accepted Answer

Estimator A’s profit margins are more variable than Estimator B’s.

Question 4

If a data set is mound-shaped and symmetric, what percentage of the data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

Approximately 95%

Question 5

A manufacturer claims the average battery life is 60 months with a standard deviation of 10 months. Using the Empirical Rule, what is the approximate probability that a randomly selected battery lasts less than 40 months?

Accepted Answer

About 2.5%

Question 6

Which formula would you use to calculate the z-score for a sample value $$x$$?

Accepted Answer

$$z = \frac{x - \bar{x}}{s}$$

Question 7

A student scores 440 on a test where the mean is 540 and the standard deviation is 100. What is the student’s z-score?

Accepted Answer

$$z = -1$$

Question 8

Which of the following best describes the 90th percentile in a data set?

Accepted Answer

It is the value below which 90% of the data falls.

Question 9

Given the data set: 55, 60, 65, 70, 75, 80, 85, 90, 95, 100. What is the 70th percentile?

Accepted Answer

88.5

Question 10

For the data set: 12, 15, 18, 20, 22, 25, 28, 30, 35, 40, what is the value of the third quartile (Q3)?

Accepted Answer

30

Question 11

If a measurement has a z-score of 2.5 in a mound-shaped distribution, what can you infer about this measurement?

Accepted Answer

It is unusually high compared to the rest of the data.

Question 12

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is always negative.

Question 13

A company’s yearly sales are at the 90th percentile among all companies. What does this indicate?

Accepted Answer

The company’s sales are higher than 90% of all companies.

Question 14

If the mean of a data set is 50 and the standard deviation is 5, what is the interval that contains approximately 68% of the data according to the Empirical Rule?

Accepted Answer

$$(45, 55)$$

Question 15

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

Accepted Answer

It is the value that divides the data set into two equal halves.

Question 16

A data set has a mean of 100 and a standard deviation of 20. What is the z-score for a value of 140?

Accepted Answer

$$z = 2$$

Question 17

Which of the following is true about the Empirical Rule?

Accepted Answer

It applies to mound-shaped, symmetric distributions.

Question 18

If a value in a data set is more than three standard deviations away from the mean, what can you conclude?

Accepted Answer

It is an extremely unusual value.

Methods for Describing Sets of Data (II): Measures of Variability and Relative Standing

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