Q: Walter’s final grade is determined by tests (40%), homework (20%), quizzes (10%), and a final exam (30%). His scores are: Tests: 83, Homework: 98, Quizzes: 90, Final Exam: 87. What is his final grade?

$$0.4 \times 83 + 0.2 \times 98 + 0.1 \times 90 + 0.3 \times 87 = 87.9$$

Q: Heather wants a final grade of 90%. Her grades are: Tests (35%): 78, Class Assignments (20%): 92, Semester Project (35%): 93, Final Exam (10%): ?. What must she score on the final exam?

$$x = \frac{90 - (0.35 \times 78 + 0.2 \times 92 + 0.35 \times 93)}{0.1} = 97$$

Question 1

Given the graph above, which line (A, B, or C) represents the mean, median, and mode of the distribution, respectively?

Accepted Answer

A: Mode, B: Median, C: Mean

Question 2

Calculate the sample mean for the following data set: 5, 6, 8, 10, 4, 6, 9.

Accepted Answer

$$\frac{5+6+8+10+4+6+9}{7} = 6.9$$

Question 3

Rutherford downloaded five songs at an average price of $$1.23. Four of the songs cost 1.29 $$each. What was the price of the fifth song?

Accepted Answer

$$1.15$$

Question 4

Which formula represents the weighted mean for a data set with values $$x_i$$ and corresponding weights $$w_i$$?

Accepted Answer

$$\overline{x}_w = \frac{\sum w_i x_i}{\sum w_i}$$

Question 5

Walter’s final grade is determined by tests (40%), homework (20%), quizzes (10%), and a final exam (30%). His scores are: Tests: 83, Homework: 98, Quizzes: 90, Final Exam: 87. What is his final grade?

Accepted Answer

$$0.4 	imes 83 + 0.2 	imes 98 + 0.1 	imes 90 + 0.3 	imes 87 = 87.9$$

Question 6

Heather wants a final grade of 90%. Her grades are: Tests (35%): 78, Class Assignments (20%): 92, Semester Project (35%): 93, Final Exam (10%): ?. What must she score on the final exam?

Accepted Answer

$$x = \frac{90 - (0.35 	imes 78 + 0.2 	imes 92 + 0.35 	imes 93)}{0.1} = 97$$

Question 7

Find the median of the following data set: 3, 4, 6, 7, 2, 8, 9.

Accepted Answer

6

Question 8

Which of the following statements about the mode is correct?

Accepted Answer

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

Question 9

Given the data set: 6, 4, 6, 1, 7, 8, 7, 2, 5, 7. What is the mode and is the data set unimodal, bimodal, or neither?

Accepted Answer

Mode: 7; Unimodal

Question 10

Which measure of center is most appropriate for the following data: T-shirt sizes (S, M, L, XL) of American women?

Accepted Answer

Mode

Question 11

Which measure of center is most appropriate for the following data: Salaries for a professional team of baseball players?

Accepted Answer

Median

Question 12

A data set is highly skewed to the right due to a few large outliers. Which measure of center should you use?

Accepted Answer

Median

Question 13

Which of the following best describes the effect of outliers on the mean?

Accepted Answer

The mean is pulled toward the outliers.

Question 14

Which of the following is true about the median?

Accepted Answer

The median divides the area of a distribution in half.

Question 15

Which measure of center is most appropriate for professor rankings from student evaluations on a scale of best, average, and worst?

Accepted Answer

Mode

Question 16

If a data set has two values that occur with the highest frequency, what is the data set called?

Accepted Answer

Bimodal

Question 17

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

Accepted Answer

The mean is always a value in the data set.

Measures of Center in Statistics: Mean, Median, and Mode

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