$$\frac{(3 \times 4) + (4 \times 3) + (3 \times 2)}{3 + 4 + 3} = \frac{12 + 12 + 6}{10} = 3.0$$

Question 1

Which of the following best describes a 'measure of center' in statistics?

Accepted Answer

A value at the center or middle of a data set.

Question 2

Given the data set: 10, 15, 20, 25, 100, which measure of center is most affected by the outlier 100?

Accepted Answer

Mean

Question 3

Which formula correctly represents the sample mean $$\bar{x}$$ for a data set with values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

A data set consists of the following values: 8, 12, 15, 20, 22. What is the median?

Accepted Answer

15

Question 5

Which of the following statements about the median is TRUE?

Accepted Answer

The median is resistant to extreme values (outliers).

Question 6

A set of exam scores is: 70, 80, 80, 90, 100. What is the mode?

Accepted Answer

80

Question 7

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

Accepted Answer

It is resistant to outliers.

Question 8

Given the data set: 5, 7, 9, 12, 15, what is the midrange?

Accepted Answer

$$\frac{15 + 5}{2} = 10$$

Question 9

Which scenario best illustrates when the mean and median are NOT meaningful statistics?

Accepted Answer

The zip codes of five famous landmarks.

Question 10

A frequency distribution has class midpoints $$x$$ and frequencies $$f. $$Which formula gives the approximate mean?

Accepted Answer

$$\frac{\sum (f \cdot x)}{\sum f}$$

Question 11

A student’s grades and credits are: A (3 credits), B (4 credits), C (3 credits). If A=4, B=3, C=2, what is the weighted mean (GPA)?

Accepted Answer

$$\frac{(3 	imes 4) + (4 	imes 3) + (3 	imes 2)}{3 + 4 + 3} = \frac{12 + 12 + 6}{10} = 3.0$$

Question 12

Which of the following is a correct interpretation of a bimodal data set?

Accepted Answer

The data set has two values that occur with the same greatest frequency.

Question 13

Why is the midrange rarely used in practice?

Accepted Answer

It is very sensitive to extreme values.

Question 14

Which of the following is the correct formula for the population mean $$\mu$$?

Accepted Answer

$$\mu = \frac{\sum x}{N}$$

Question 15

If a data set has values: 2, 4, 6, 8, 10, and 12, what is the median?

Accepted Answer

$$\frac{6 + 8}{2} = 7$$

Question 16

Which of the following is a resistant measure of center?

Accepted Answer

Median

Question 17

A data set has values: 3, 7, 7, 7, 10, 12. What is the mode?

Accepted Answer

7

Question 18

Which of the following is an example where the mean is NOT a meaningful statistic?

Accepted Answer

Calculating the mean of jersey numbers of a football team.

Question 19

If a data set has no repeated values, what can be said about its mode?

Accepted Answer

There is no mode.

Question 20

Which of the following best describes a weighted mean?

Accepted Answer

A mean where each data value is multiplied by a weight before summing.

Measures of Center in Descriptive Statistics

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