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

$$\frac{(10 \times 2) + (20 \times 3) + (30 \times 5)}{2 + 3 + 5}$$

Q: A student receives grades of A (4 points) in a 3-credit course, B (3 points) in a 4-credit course, and C (2 points) in a 3-credit course. What is the weighted mean (GPA)?

$$\frac{(4 \times 3) + (3 \times 4) + (2 \times 3)}{3 + 4 + 3}$$

Q: Given the following grouped data: Class midpoints: 5, 15, 25; Frequencies: 2, 4, 4. What is the mean of the frequency distribution?

$$\frac{(5 \times 2) + (15 \times 4) + (25 \times 4)}{2 + 4 + 4}$$

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 sample data: 12, 15, 15, 18, 20, what is the median?

Accepted Answer

$$15$$

Question 3

A teacher records the following grades for five students: 70, 80, 85, 90, 100. If the student who scored 100 drops the class, what happens to the mean?

Accepted Answer

The mean decreases.

Question 4

Which formula is used to calculate the weighted mean?

Accepted Answer

$$\frac{\sum xw}{\sum w}$$

Question 5

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

Accepted Answer

$$\frac{(10 	imes 2) + (20 	imes 3) + (30 	imes 5)}{2 + 3 + 5}$$

Question 6

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 7

A distribution is described as symmetric. Which of the following is true?

Accepted Answer

The mean, median, and mode are all equal.

Question 8

In a right-skewed (positively skewed) distribution, which of the following is the correct order from least to greatest?

Accepted Answer

Mode, Median, Mean

Question 9

A data set has the following values: 5, 7, 7, 8, 10, 12, 12, 12, 15. What is the mode?

Accepted Answer

$$12$$

Question 10

Which of the following best describes a uniform distribution?

Accepted Answer

All entries have approximately equal frequencies.

Question 11

A student receives grades of A (4 points) in a 3-credit course, B (3 points) in a 4-credit course, and C (2 points) in a 3-credit course. What is the weighted mean (GPA)?

Accepted Answer

$$\frac{(4 	imes 3) + (3 	imes 4) + (2 	imes 3)}{3 + 4 + 3}$$

Question 12

Which scenario best illustrates when the median is a better measure of central tendency than the mean?

Accepted Answer

When the data set contains outliers.

Question 13

If a data set has two values that occur with the same highest frequency, the data set is:

Accepted Answer

Bimodal

Question 14

Given the following grouped data: Class midpoints: 5, 15, 25; Frequencies: 2, 4, 4. What is the mean of the frequency distribution?

Accepted Answer

$$\frac{(5 	imes 2) + (15 	imes 4) + (25 	imes 4)}{2 + 4 + 4}$$

Question 15

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

Accepted Answer

Range

Question 16

A distribution has a long tail to the left. Which of the following is true?

Accepted Answer

The mean is to the left of the median.

Question 17

Which of the following is the correct formula for the sample mean?

Accepted Answer

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

Question 18

A data set contains the values: 2, 4, 4, 6, 8, 10, 100. Which measure of central tendency is most representative of a typical value in this set?

Accepted Answer

Median

Question 19

Which of the following statements is true about the mode?

Accepted Answer

The mode is the value that occurs with the greatest frequency.

Question 20

If a data set is uniform, which of the following is true?

Accepted Answer

All values occur with approximately equal frequency.

Descriptive Statistics: Measures of Central Tendency and Distribution Shapes

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