Q: A student’s grades and credits are: A (3 credits), B (4 credits), C (3 credits), F (2 credits). If A=4, B=3, C=2, F=0, what is the weighted mean (GPA)?

$$\frac{(4 \times 3) + (3 \times 4) + (2 \times 3) + (0 \times 2)}{3 + 4 + 3 + 2} = \frac{12 + 12 + 6 + 0}{12} = \frac{30}{12} = 2.5$$

Q: The midrange of a data set is calculated as:

$$\frac{\text{Maximum value} + \text{Minimum value}}{2}$$

Q: If the mean of a data set is $$50$$ and the standard deviation is $$5$$, according to the Range Rule of Thumb, what is the approximate range of usual values?

$$50 \pm 2 \times 5 = [40, 60]$$

Q: A frequency distribution has the following intervals and frequencies: 75–124 (11), 125–174 (24), 175–224 (10), 225–274 (3), 275–324 (2). What is the formula to estimate the mean from this grouped data?

$$\frac{\sum (f \times x)}{\sum f}$$,\ where\ x\ is\ the\ class\ midpoint

Question 1

Which of the following best describes the meaning of the mean ($$\bar{x}) in a $$data set?

Accepted Answer

The arithmetic average of all values in the data set.

Question 2

Given the data set: 188, 206, 208, 237, 239, 256, 256, 262, 301, 301, 306, what is the median?

Accepted Answer

$$256$$

Question 3

Which measure of center is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 4

If a data set has the following values: 10, 12, 12, 15, 18, what is the mode?

Accepted Answer

$$12$$

Question 5

A student’s grades and credits are: A (3 credits), B (4 credits), C (3 credits), F (2 credits). If A=4, B=3, C=2, F=0, what is the weighted mean (GPA)?

Accepted Answer

$$\frac{(4 	imes 3) + (3 	imes 4) + (2 	imes 3) + (0 	imes 2)}{3 + 4 + 3 + 2} = \frac{12 + 12 + 6 + 0}{12} = \frac{30}{12} = 2.5$$

Question 6

What is the formula for the sample standard deviation $$s$$?

Accepted Answer

$$s = \sqrt{\frac{\sum (x - \bar{x})^2$}{n-1}}$$

Question 7

Given the data set: 14.1, 22.4, 23.1, 38.5, 55.6, what is the range?

Accepted Answer

$$55.6 - 14.1 = 41.5$$

Question 8

Which of the following statements about variance is TRUE?

Accepted Answer

Variance is always zero or positive.

Question 9

The midrange of a data set is calculated as:

Accepted Answer

$$\frac{	ext{Maximum value} + 	ext{Minimum value}}{2}$$

Question 10

If the mean of a data set is $$50$$ and the standard deviation is $$5$$, according to the Range Rule of Thumb, what is the approximate range of usual values?

Accepted Answer

$$50 \pm 2 	imes 5 = [40, 60]$$

Question 11

Which measure is best for comparing the relative variation between two data sets with different units?

Accepted Answer

Coefficient of Variation (CV)

Question 12

A frequency distribution has the following intervals and frequencies: 75–124 (11), 125–174 (24), 175–224 (10), 225–274 (3), 275–324 (2). What is the formula to estimate the mean from this grouped data?

Accepted Answer

$$\frac{\sum (f 	imes x)}{\sum f}$$,\ where\ x\ is\ the\ class\ midpoint

Question 13

If a data set has a mean of $$100$$ and a standard deviation of $$15$$, which value would be considered significantly high according to the Range Rule of Thumb?

Accepted Answer

$$140$$

Question 14

Which of the following is NOT a measure of center?

Accepted Answer

Standard deviation

Question 15

If all values in a data set are the same, what is the value of the standard deviation?

Accepted Answer

Zero

Question 16

Which of the following best describes the effect of adding an extreme value (outlier) to a data set?

Accepted Answer

It increases the mean more than the median.

Question 17

Refer to the image provided. According to the Range Rule of Thumb, which interval contains values that are NOT considered significant?

Accepted Answer

$$\mu - 2\sigma to$$ $$\mu + 2\sigma$$

Measures of Center and Variation in Introductory Statistics

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