Q: A student’s grades are weighted as follows: Homework 15%, Quizzes 15%, Exam 1 20%, Exam 2 20%, Final 30%. If the student scores 95, 90, 80, 70, and 60 respectively, what is the weighted mean?

$$0.15 \times 95 + 0.15 \times 90 + 0.20 \times 80 + 0.20 \times 70 + 0.30 \times 60 = 75.5$$

Q: Which of the following statements about the midrange is true?

It is calculated as $$\frac{\text{max} + \text{min}}{2}.$$

Question 1

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

Accepted Answer

The balancing point of the data set, calculated as the sum of all values divided by the number of values.

Question 2

Given the following data set: 2, 4, 7, 10, 15, what is the midrange?

Accepted Answer

$$\frac{2+15}{2} = 8.5$$

Question 3

A sample of 8 exam scores is: 70, 72, 75, 80, 85, 90, 92, 100. What is the median?

Accepted Answer

$$\frac{80+85}{2} = 82.5$$

Question 4

Which measure of center is most resistant to outliers?

Accepted Answer

Median

Question 5

A data set is right-skewed. Which of the following is the correct order of the measures of center from left to right?

Accepted Answer

Mode, Median, Mean, Midrange

Question 6

If a data set has two values that occur with the highest frequency, what is the correct term for this data set?

Accepted Answer

Bimodal

Question 7

A student’s grades are weighted as follows: Homework 15%, Quizzes 15%, Exam 1 20%, Exam 2 20%, Final 30%. If the student scores 95, 90, 80, 70, and 60 respectively, what is the weighted mean?

Accepted Answer

$$0.15 	imes 95 + 0.15 	imes 90 + 0.20 	imes 80 + 0.20 	imes 70 + 0.30 	imes 60 = 75.5$$

Question 8

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

Accepted Answer

It is always one of the data values.

Question 9

In a symmetric distribution, which of the following is true?

Accepted Answer

Mean, median, mode, and midrange are all equal.

Question 10

A real estate agent reports the median sale price of homes in a city rather than the mean. What is the most likely reason for this choice?

Accepted Answer

The median is less affected by extremely high or low sale prices.

Question 11

If a data set has the following values: 3, 3, 4, 5, 8, 10, 12, what is the mode?

Accepted Answer

3

Question 12

Which of the following is the correct formula for the sample mean $$\bar{x} of$$ $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 13

A data set has the following values: 2, 4, 6, 8, 100. Which measure of center is most affected by the outlier?

Accepted Answer

Mean

Question 14

Which of the following statements about the midrange is true?

Accepted Answer

It is calculated as $$\frac{	ext{max} + 	ext{min}}{2}.$$

Question 15

If a data set is left-skewed, which measure of center is typically the largest?

Accepted Answer

Midrange

Question 16

A teacher wants to report a measure of center for a set of test scores that includes several extremely low outliers. Which measure should the teacher use?

Accepted Answer

Median

Question 17

Which of the following is a correct statement about the mode?

Accepted Answer

A data set may have no mode, one mode, or more than one mode.

Question 18

A sample of 5 values is: 10, 12, 14, 16, 18. What is the mean?

Accepted Answer

$$\frac{10+12+14+16+18}{5} = 14$$

Question 19

Which of the following best explains why the midrange is rarely used in practice?

Accepted Answer

It is highly sensitive to extreme values (outliers).

Question 20

If the data values are: 5, 7, 7, 8, 10, 12, 15, what is the median?

Accepted Answer

8

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

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