Q: Which formula correctly calculates the range of a data set?

$$\text{Range} = (\text{Max. data entry}) - (\text{Min. data entry})$$

Q: A data set has a mean of 50 and a standard deviation of 5. What is the coefficient of variation (CV) for this population data set?

$$CV = \frac{5}{50} \times 100\% = 10\%$$

Q: A value in a data set is considered an outlier if it is less than $$Q1 - 1.5 \times IQR or $$greater than $$Q3 + 1.5 \times IQR. If$$ $$Q1 = 10$$, $$Q3 = 30$$, and $$IQR = 20$$, what is the upper bound for outliers?

$$Q3 + 1.5 \times IQR = 30 + 1.5 \times 20 = 60$$

Q: Which formula is used to calculate the percentile of a specific data entry $$x$$?

$$\text{Percentile of } x = \frac{\text{number of data entries less than } x}{\text{total number of data entries}} \times 100$$

Q: Which formula gives the classical (theoretical) probability of event $$E$$?

$$P(E) = \frac{\text{Number of outcomes in event } E}{\text{Number of outcomes in sample space}}$$

Q: If events A and B are independent, what is the probability that both A and B occur?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Question 1

Which formula correctly calculates the range of a data set?

Accepted Answer

$$	ext{Range} = (	ext{Max. data entry}) - (	ext{Min. data entry})$$

Question 2

A company has two departments, A and B, both with the same mean salary but different spreads. Department A's salaries are tightly clustered, while Department B's are more spread out. Which measure best captures this difference?

Accepted Answer

Standard deviation

Question 3

Given a population data set with entries $$x_1$$, $$x_2$$, ..., x_N$$ and mean $$\mu$$, which formula gives the population variance?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum (x - \mu)^2$}{N}$$

Question 4

Which statement about standard deviation is FALSE?

Accepted Answer

Standard deviation can be negative.

Question 5

For a sample data set, which formula correctly calculates the sample variance?

Accepted Answer

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

Question 6

A data set has a mean of 50 and a standard deviation of 5. What is the coefficient of variation (CV) for this population data set?

Accepted Answer

$$CV = \frac{5}{50} 	imes 100\% = 10\%$$

Question 7

Which of the following is NOT part of the five-number summary required for a box and whisker plot?

Accepted Answer

Mean

Question 8

If the first quartile (Q1) of a data set is 20 and the third quartile (Q3) is 40, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 40 - 20 = 20$$

Question 9

A value in a data set is considered an outlier if it is less than $$Q1 - 1.5 	imes IQR or $$greater than $$Q3 + 1.5 	imes IQR. If$$ $$Q1 = 10$$, $$Q3 = 30$$, and $$IQR = 20$$, what is the upper bound for outliers?

Accepted Answer

$$Q3 + 1.5 	imes IQR = 30 + 1.5 	imes 20 = 60$$

Question 10

Which formula is used to calculate the percentile of a specific data entry $$x$$?

Accepted Answer

$$	ext{Percentile of } x = \frac{	ext{number of data entries less than } x}{	ext{total number of data entries}} 	imes 100$$

Question 11

A student scored 85 on a test where the mean is 75 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 12

According to the Empirical Rule, approximately what percent of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 13

Chebyshev's Theorem states that for any data set, at least what percent of the data lies within three standard deviations of the mean?

Accepted Answer

88.9%

Question 14

Which formula gives the classical (theoretical) probability of event $$E$$?

Accepted Answer

$$P(E) = \frac{	ext{Number of outcomes in event } E}{	ext{Number of outcomes in sample space}}$$

Question 15

If a coin is tossed 1000 times, the proportion of heads observed approaches 0.5. This illustrates which statistical law?

Accepted Answer

Law of Large Numbers

Question 16

If $$P(E) = 0.3$$, what is the probability of the complementary event $$E'$$?

Accepted Answer

$$P(E') = 1 - P(E) = 0.7$$

Question 17

Which of the following is TRUE about independent events A and B?

Accepted Answer

$$P(B|A) = P(B)$$

Question 18

If events A and B are independent, what is the probability that both A and B occur?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Descriptive Statistics and Probability: Measures of Variation, Probability Concepts, and Counting Rules

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