Q: A student receives the following grades and credit hours: A (4 points, 3 credits), B (3 points, 4 credits), C (2 points, 2 credits). What is the weighted mean (GPA)?

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

Q: A frequency distribution for screen time (in minutes) is given. The midpoints are 150, 200, 250, 300, and the frequencies are 2, 5, 8, 5. What is the estimated mean screen time?

$$\frac{(150 \times 2) + (200 \times 5) + (250 \times 8) + (300 \times 5)}{2+5+8+5}$$

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, 20, what is the median?

Accepted Answer

$$15$$

Question 3

A teacher records the following test scores: 70, 85, 90, 90, 95. What is the mode?

Accepted Answer

$$90$$

Question 4

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 5

A data set has the following values: 5, 7, 7, 8, 10, 12, 100. Which measure best represents the center of this data set?

Accepted Answer

Median

Question 6

If a distribution is symmetric and unimodal, which of the following is true?

Accepted Answer

The mean, median, and mode are equal.

Question 7

What is the formula for the weighted mean of a data set?

Accepted Answer

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

Question 8

A student receives the following grades and credit hours: A (4 points, 3 credits), B (3 points, 4 credits), C (2 points, 2 credits). What is the weighted mean (GPA)?

Accepted Answer

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

Question 9

Which of the following distributions is described as having all entries with approximately equal frequencies?

Accepted Answer

Uniform distribution

Question 10

In a frequency distribution, how do you estimate the mean using class midpoints and frequencies?

Accepted Answer

$$\frac{\sum xf}{n}$$

Question 11

A data set is said to be skewed left if:

Accepted Answer

The mean is less than the median.

Question 12

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

Accepted Answer

It is always unique for any data set.

Question 13

A hospital records the number of patients seen each day for a week: 20, 22, 22, 23, 25, 25, 25. What is the mode?

Accepted Answer

$$25$$

Question 14

Which measure of central tendency should be used for a data set with extreme outliers?

Accepted Answer

Median

Question 15

A distribution is positively skewed if:

Accepted Answer

The mean is greater than the median.

Question 16

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

Accepted Answer

There is no mode.

Question 17

A frequency distribution for screen time (in minutes) is given. The midpoints are 150, 200, 250, 300, and the frequencies are 2, 5, 8, 5. What is the estimated mean screen time?

Accepted Answer

$$\frac{(150 	imes 2) + (200 	imes 5) + (250 	imes 8) + (300 	imes 5)}{2+5+8+5}$$

Question 18

Which of the following is a real-world example where the weighted mean is more appropriate than the simple mean?

Accepted Answer

Calculating a student's GPA based on grades and credit hours.

Question 19

If a data set is described as bimodal, what does this mean?

Accepted Answer

There are two values that occur with the same greatest frequency.

Question 20

Which of the following statements about the mean of grouped data is correct?

Accepted Answer

It is an estimate based on class midpoints and frequencies.

Measures of Central Tendency and the Shape of Distributions

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