Q: Which formula is used to calculate the coefficient of variation (CV) for a sample?

$$CV = \frac{S}{\bar{x}} \times 100\%$$

Question 1

Given the following frequency distribution of exam scores, what is the mean score?

Score | Frequency
60    | 2
70    | 3
80    | 5
90    | 4

Calculate the mean using the formula:
$$
	ext{Mean} = \frac{\sum f_i x_i}{\sum f_i}
$$

Accepted Answer

Mean = 78.0

Question 2

A researcher collects the following sample data: 5, 7, 9, 10, 14. What is the sample variance?
Use the formula:
$$
S^2$ = \frac{\sum (x_i - \bar{x})^2$}{n-1}
$$

Accepted Answer

Sample variance = 12.3

Question 3

Which of the following statements about the range is correct?

Accepted Answer

The range is the difference between the maximum and minimum values in a dataset.

Question 4

A boxplot of exam scores shows a long whisker on the right side. What does this indicate about the distribution?

Accepted Answer

The distribution is right-skewed.

Question 5

Given a sample with values 2, 4, 6, 8, 10, what is the sample standard deviation?
Use the formula:
$$
S = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}
$$

Accepted Answer

Sample standard deviation = 3.16

Question 6

A student scored 85 on a test where the mean was 75 and the standard deviation was 5. What is the z-score for the student?
Use the formula:
$$
z = \frac{x - \mu}{\sigma}
$$

Accepted Answer

z = 2.0

Question 7

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

Accepted Answer

Range

Question 8

If the probability of event A is 0.3 and the probability of event B is 0.5, and A and B are independent, what is the probability that both A and B occur?
Use the multiplication rule:
$$
P(A \cap B) = P(A) 	imes P(B)
$$

Accepted Answer

0.15

Question 9

Which formula is used to calculate the coefficient of variation (CV) for a sample?

Accepted Answer

$$CV = \frac{S}{\bar{x}} 	imes 100\%$$

Question 10

A dataset has the following five-number summary: Min = 12, Q1 = 18, Median = 25, Q3 = 32, Max = 40. What is the interquartile range (IQR)?
Use the formula:
$$
IQR = Q_3$ - Q_1$
$$

Accepted Answer

IQR = 14

Question 11

Which of the following best describes a dependent event in probability?

Accepted Answer

The occurrence of one event affects the probability of the other.

Question 12

A bag contains 4 red balls and 6 blue balls. If two balls are drawn without replacement, what is the probability that both are red?
Use:
$$
P(	ext{both red}) = \frac{4}{10} 	imes \frac{3}{9}
$$

Accepted Answer

0.133

Question 13

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

Accepted Answer

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

Question 14

If the range rule of thumb estimates the standard deviation as $$\sigma \approx \frac{	ext{Range}}{4}$$, what is the estimated standard deviation for a dataset with a minimum of 10 and a maximum of 50?

Accepted Answer

12.5

Question 15

Which of the following is NOT true about the median?

Accepted Answer

The median is affected by extreme values.

Question 16

A hospital records the number of patients admitted each day for a week: 12, 15, 13, 17, 14, 16, 13. What is the mode?

Accepted Answer

13

Question 17

Which of the following is a complementary event to 'rolling a 6 on a fair die'?

Accepted Answer

Rolling any number except 6

Question 18

A sample of 8 students has test scores: 70, 75, 80, 85, 90, 95, 100, 105. What is the percentile rank of the score 90?

Accepted Answer

62.5th percentile

Question 19

Which formula is used to calculate the sample variance?

Accepted Answer

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

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