Q: Walter’s US history 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% in her sculpting class. 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?

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 new songs. The average cost was $$1.23. Four songs cost 1.29 $$each. What was the price of the fifth song?

Accepted Answer

$$1.05$$

Question 4

Walter’s US history 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 5

Heather wants a final grade of 90% in her sculpting class. 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 6

What is the median of the following data set: 3, 4, 6, 7, 2, 8, 9?

Accepted Answer

6

Question 7

What is the mode of the following data set: 6, 4, 6, 1, 7, 8, 7, 2, 5, 7?

Accepted Answer

7

Question 8

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 9

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

Accepted Answer

Median

Question 10

A data set is highly skewed to the right. Which measure of center is most likely to be pulled in the direction of the skew?

Accepted Answer

Mean

Question 11

Which of the following statements is true about the mode?

Accepted Answer

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

Question 12

If a data set contains outliers, which measure of center is generally the most appropriate to use?

Accepted Answer

Median

Question 13

Which of the following is the formula for the sample mean?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 14

Which of the following is the formula for the weighted mean?

Accepted Answer

$$\bar{x}_w = \frac{\sum_{i=1}^{n} x_i w_i}{\sum_{i=1}^{n} w_i}$$

Question 15

A data set has two values that occur with the highest and equal frequency. How is this data set described?

Accepted Answer

Bimodal

Question 16

Which measure of center divides the area under a distribution in half?

Accepted Answer

Median

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

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