Question 1

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

Accepted Answer

The sum of all values divided by the number of values.

Question 2

Given the sample data set: 5, 11, 12, 14, 13, what is the mean?

Accepted Answer

$$ \frac{5 + 11 + 12 + 14 + 13}{5} = 12 $$

Question 3

A population consists of the values: 1.5, 1.8, 1.4, 1.6, 1.4, 1.8, 1.7, 1.6. What is the mean of this population?

Accepted Answer

$$ \frac{1.5 + 1.8 + 1.4 + 1.6 + 1.4 + 1.8 + 1.7 + 1.6}{8} = 1.6 $$

Question 4

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean is a measure of center that can be influenced by outliers.

Question 5

A sample of students in a college class has the following ages: 19, 20, 20, 21, 21, 21, 22, 22, 23, 24. What is the mean age?

Accepted Answer

$$ \frac{19 + 20 + 20 + 21 + 21 + 21 + 22 + 22 + 23 + 24}{10} = 21.3 $$

Question 6

If a single extremely high value is added to a data set, what is the most likely effect on the mean?

Accepted Answer

The mean will increase.

Question 7

A researcher collects the following heart rates (beats per minute) from a sample of adult males: 74, 78, 80, 84, 90, 96, 98, 100, 102. What is the mean heart rate for this sample?

Accepted Answer

$$ \frac{74 + 78 + 80 + 84 + 90 + 96 + 98 + 100 + 102}{9} = 89.1 $$

Question 8

In a study, the mean heart rate for females is found to be 81.4 beats per minute, and for males it is 79.2 beats per minute. Which of the following is a correct interpretation?

Accepted Answer

On average, females have a higher heart rate than males.

Question 9

Which formula correctly represents the calculation of the mean for a sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$ \bar{x} = \frac{x_1$ + x_2$ + ... + x_n}{n} $$

Question 10

A data set consists of the values: 10, 12, 14, 16, 18. If the value 100 is added to the data set, what happens to the mean?

Accepted Answer

The mean increases significantly.

Question 11

A sample of 8 students has the following test scores: 70, 75, 80, 85, 90, 95, 100, 105. What is the mean score?

Accepted Answer

$$ \frac{70 + 75 + 80 + 85 + 90 + 95 + 100 + 105}{8} = 87.5 $$

Question 12

If the mean of a data set is 20 and a new value of 100 is added, what will happen to the mean?

Accepted Answer

The mean will increase.

Question 13

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

Accepted Answer

It always equals the median.

Question 14

A data set contains the values: 2, 4, 6, 8, 10. If each value is increased by 3, what is the new mean?

Accepted Answer

The new mean is the original mean plus 3.

Question 15

A sample of 5 patients has cholesterol levels of 180, 190, 200, 210, and 220 mg/dL. What is the mean cholesterol level?

Accepted Answer

$$ \frac{180 + 190 + 200 + 210 + 220}{5} = 200 $$

Question 16

If the mean heart rate for a group of males is 79.2 and for females is 81.4, what is the difference in mean heart rates?

Accepted Answer

$$ 81.4 - 79.2 = 2.2 $$

Understanding and Calculating the Mean in Statistics

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