Q: A student receives grades with the following weights: A (4 points, 2 classes), B (3 points, 3 classes), C (2 points, 1 class). What is the weighted mean (GPA)?

$$\frac{(4 \times 2) + (3 \times 3) + (2 \times 1)}{2+3+1} = \frac{8+9+2}{6} = \frac{19}{6} \approx 3.17$$

Question 1

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

Accepted Answer

The sum of all data entries divided by the number of entries.

Question 2

Given the data set: 12, 15, 15, 18, 21, what is the median?

Accepted Answer

15

Question 3

A sample of weights (in pounds) is: 150, 160, 170, 180, 190. What is the mean weight?

Accepted Answer

$$\frac{150+160+170+180+190}{5} = 170$$

Question 4

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 5

A student receives grades with the following weights: A (4 points, 2 classes), B (3 points, 3 classes), C (2 points, 1 class). What is the weighted mean (GPA)?

Accepted Answer

$$\frac{(4 	imes 2) + (3 	imes 3) + (2 	imes 1)}{2+3+1} = \frac{8+9+2}{6} = \frac{19}{6} \approx 3.17$$

Question 6

If a data set has no repeated values, which statement is true?

Accepted Answer

The data set has no mode.

Question 7

A frequency distribution has midpoints $$x_i$$ and frequencies $$f_i. $$Which formula estimates the mean?

Accepted Answer

$$\frac{\sum x_i f_i}{\sum f_i}$$

Question 8

Which distribution shape is described as having equal frequencies for all classes?

Accepted Answer

Uniform

Question 9

In a positively skewed distribution, which relationship is true?

Accepted Answer

Mean \u003e Median

Question 10

A data set is: 10, 12, 14, 16, 18, 100. Which measure best describes a typical entry?

Accepted Answer

Median

Question 11

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 12

If a data set is skewed left, what is the likely order of mean and median?

Accepted Answer

Mean is to the left of the median.

Question 13

A sample of screen times (in minutes) is grouped into classes. Why is the mean calculated from midpoints only an estimate?

Accepted Answer

Midpoints do not represent the actual values of all data entries.

Question 14

Which scenario best illustrates the disadvantage of using the mean?

Accepted Answer

A data set with one value much higher than the rest.

Question 15

If a data set is symmetric, which statement is true?

Accepted Answer

Mean, median, and mode are all equal.

Question 16

A political survey records responses: Democrat, Republican, Independent, Democrat, Republican, Democrat. What is the mode?

Accepted Answer

Democrat

Question 17

Which measure of central tendency is most appropriate for categorical data?

Accepted Answer

Mode

Question 18

A data set has two values that occur with the same greatest frequency. What is this called?

Accepted Answer

Bimodal

Question 19

Which formula represents the sample mean for $$n$$ entries $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 20

A data set is: 5, 7, 7, 8, 10, 12. What is the mode?

Accepted Answer

7

Descriptive Statistics: Measures of Central Tendency

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