Q: A student’s GPA is calculated using a weighted mean. If the student earned grades of A (4 points) in a 4-credit course, B (3 points) in a 3-credit course, and C (2 points) in a 2-credit course, what is the GPA?

$$\frac{4 \times 4 + 3 \times 3 + 2 \times 2}{4 + 3 + 2} = 3.22$$

Question 1

Which of the following is the best measure of central tendency to use for a data set that is highly skewed to the right, such as household income in a large city?

Accepted Answer

Median

Question 2

A pharmaceutical company wants to include in a study only those candidates whose cholesterol levels are between 1.5 and 3 standard deviations above the mean. If the mean cholesterol is 200 mg and the standard deviation is 25 mg, what is the range of cholesterol levels for inclusion?

Accepted Answer

$$237.5 - 275$$

Question 3

Given the following exam scores: 62, 68, 71, 74, 77, 82, 84, 88, 90, 94, what is the median score?

Accepted Answer

80

Question 4

Which of the following statements about the mean and median is TRUE?

Accepted Answer

The median is not affected by extreme values.

Question 5

A sample of house prices in thousands of dollars is: 75, 119, 95, 126, 78, 90, 10, 47, 65, 125, 225, 180, 300, 120, 186, 30, 35, 116, 100, 88, 90. What is the range of this data set?

Accepted Answer

$$290$$

Question 6

Which of the following formulas correctly represents the sample standard deviation?

Accepted Answer

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

Question 7

If a distribution is bell-shaped and has a mean of 50 and a standard deviation of 5, according to the Empirical Rule, approximately what percentage of data falls between 40 and 60?

Accepted Answer

95%

Question 8

A student scored 85 on a test where the class mean was 80 and the standard deviation was 5. What is the student's z-score?

Accepted Answer

$$z = 1$$

Question 9

Which measure of dispersion is most affected by extreme values?

Accepted Answer

Range

Question 10

A frequency distribution for birth weights (in grams) is given. To approximate the mean from grouped data, which formula should you use?

Accepted Answer

$$\bar{x} = \frac{\sum x_i f_i}{\sum f_i}$$

Question 11

Which of the following best describes a bimodal distribution?

Accepted Answer

A distribution with two peaks

Question 12

If the mean is greater than the median in a data set, what is the likely shape of the distribution?

Accepted Answer

Skewed right

Question 13

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

Accepted Answer

It is resistant to outliers.

Question 14

A boxplot is most useful for which of the following tasks?

Accepted Answer

Identifying outliers and visualizing the five-number summary

Question 15

Which of the following is the formula for the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 16

Chebyshev’s Inequality states that for any data set, at least what percentage of values lie within $$k = 2$$ standard deviations of the mean?

Accepted Answer

75%

Question 17

A student’s GPA is calculated using a weighted mean. If the student earned grades of A (4 points) in a 4-credit course, B (3 points) in a 3-credit course, and C (2 points) in a 2-credit course, what is the GPA?

Accepted Answer

$$\frac{4 	imes 4 + 3 	imes 3 + 2 	imes 2}{4 + 3 + 2} = 3.22$$

Question 18

Which of the following best describes the mode?

Accepted Answer

The value that occurs most frequently in a data set

Question 19

If a data set has a mean of 100 and a standard deviation of 15, what is the z-score for a value of 130?

Accepted Answer

$$z = 2$$

Question 20

Which of the following is NOT included in the five-number summary?

Accepted Answer

Mean

Measures of Central Tendency and Dispersion in Statistics

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