Q: A hospital records the birth weights of newborns. The mean is 6.5 lbs and the standard deviation is 1.4 lbs. According to the Range Rule of Thumb, what is the lowest weight considered significantly high?

$$6.5 + 2 \times 1.4 = 9.3$$ lbs

Q: A sample of wait times at a restaurant has a mean of 8 minutes and a standard deviation of 2.5 minutes. According to the Empirical Rule, what is the range of wait times that contains approximately 95% of the data?

$$8 \pm 2 \times 2.5 = 3 to$$ $$13$$ minutes

Question 1

A sample of exam scores is: 72, 85, 90, 68, 75. What is the mean of this data set? Use the formula $$\bar{x} = \frac{\sum x}{n}.$$

Accepted Answer

Question 2

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean uses all values in the data set and can be greatly affected by extreme values.

Question 3

Given the data set {5, 10, 14, 12, 3, 76}, which measure of center is most affected by the value 76?

Accepted Answer

Mean

Question 4

A hospital records the birth weights of newborns. The mean is 6.5 lbs and the standard deviation is 1.4 lbs. According to the Range Rule of Thumb, what is the lowest weight considered significantly high?

Accepted Answer

$$6.5 + 2 	imes 1.4 = 9.3$$ lbs

Question 5

Which of the following is the correct formula for the sample standard deviation?

Accepted Answer

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

Question 6

A data set is: 3, 5, 7, 9, 11. What is the median?

Accepted Answer

7

Question 7

A sample of 500 books has a mean of 312 pages and a standard deviation of 26 pages. According to the Empirical Rule, what percentage of books have between 286 and 338 pages?

Accepted Answer

68%

Question 8

Which of the following best describes the mode?

Accepted Answer

The value that occurs most frequently in a data set.

Question 9

A data set of home prices (in thousands): 275, 229, 850, 240, 305, 287, 310, 342. Which measure of center is more representative of the sample?

Accepted Answer

Median, because it is resistant to the outlier 850.

Question 10

Given the data set {2, 4, 4, 6, 8, 8, 8, 10}, what is the mode?

Accepted Answer

8

Question 11

A sample of wait times at a restaurant has a mean of 8 minutes and a standard deviation of 2.5 minutes. According to the Empirical Rule, what is the range of wait times that contains approximately 95% of the data?

Accepted Answer

$$8 \pm 2 	imes 2.5 = 3 to$$ $$13$$ minutes

Question 12

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

Accepted Answer

It is resistant to outliers.

Question 13

A data set has a mean of 50 and a standard deviation of 5. What is the z-score of a value 60?

Accepted Answer

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

Question 14

The 1st quartile (Q1) and 3rd quartile (Q3) of a data set are 25 and 45, respectively. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 20$$

Question 15

A boxplot displays which of the following?

Accepted Answer

The five-number summary: minimum, Q1, median, Q3, maximum

Question 16

If a data set is symmetric and has no outliers, which measure of center is generally preferred?

Accepted Answer

Mean

Question 17

A student scores at the 90th percentile on a standardized test. What does this mean?

Accepted Answer

The student scored higher than 90% of the test takers.

Question 18

Which of the following is a real-life example where the median is a better measure of center than the mean?

Accepted Answer

Annual incomes in a city with a few billionaires.

Question 19

A data set has the following values: 2, 4, 6, 8, 10, 12. What is the percentile rank of the value 8?

Accepted Answer

66.7%

Descriptive Measures in Statistics: Mean, Median, Mode, and Standard Deviation

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