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)?

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

Q: A frequency distribution has midpoints 10, 20, 30 with frequencies 2, 3, 5. What is the estimated mean?

$$\frac{(10 \times 2) + (20 \times 3) + (30 \times 5)}{2 + 3 + 5} = \frac{20 + 60 + 150}{10} = \frac{230}{10} = 23$$

Question 1

Which measure of central tendency is most affected by outliers in a data set?

Accepted Answer

Mean

Question 2

A sample of weights (in pounds) is: 150, 160, 170, 180, 300. What is the median weight?

Accepted Answer

170

Question 3

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

Accepted Answer

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

Question 4

In a frequency distribution, the mean is estimated using class midpoints and frequencies. Which formula is used?

Accepted Answer

$$\bar{x} = \frac{\sum x f}{\sum f}$$

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

Which distribution shape is described as having all entries with equal or approximately equal frequencies?

Accepted Answer

Uniform distribution

Question 7

If a data set is symmetric and unimodal, which statement is true about its mean, median, and mode?

Accepted Answer

Mean = Median = Mode

Question 8

A data set has the values: 10, 12, 12, 14, 16, 18, 20. What is the mode?

Accepted Answer

12

Question 9

Which measure of central tendency is best used when a data set contains outliers?

Accepted Answer

Median

Question 10

A distribution is skewed right. Which of the following is most likely true?

Accepted Answer

Mean \u003e Median \u003e Mode

Question 11

In a sample of ages: 18, 19, 20, 21, 22, 65, which measure best describes a typical age?

Accepted Answer

Median

Question 12

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

Accepted Answer

Range

Question 13

If a data set has two entries with the greatest frequency, what is the mode?

Accepted Answer

Bimodal

Question 14

A frequency distribution has midpoints 10, 20, 30 with frequencies 2, 3, 5. What is the estimated mean?

Accepted Answer

$$\frac{(10 	imes 2) + (20 	imes 3) + (30 	imes 5)}{2 + 3 + 5} = \frac{20 + 60 + 150}{10} = \frac{230}{10} = 23$$

Question 15

Which scenario best illustrates the use of a weighted mean?

Accepted Answer

Calculating a student's GPA based on course credits

Question 16

A data set is: 5, 7, 7, 8, 9, 10, 12. Which statement about the distribution is correct?

Accepted Answer

It is symmetric

Question 17

Which of the following best describes a normal distribution?

Accepted Answer

Symmetric and unimodal

Question 18

If a data set has no repeated entries, what is the mode?

Accepted Answer

No mode

Question 19

Which measure of central tendency is most reliable when all data entries are taken into account and there are no outliers?

Accepted Answer

Mean

Question 20

A data set is: 2, 4, 6, 8, 10. What is the mean?

Accepted Answer

$$\frac{2 + 4 + 6 + 8 + 10}{5} = \frac{30}{5} = 6$$

Measures of Central Tendency in Descriptive Statistics

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