Q: Given the data set: 10, 60, 50, 30, 40, 20, what is the range?

$$\text{Range} = 60 - 10 = 50$$

Q: What is the coefficient of variation (CV) for a sample with mean $$\bar{X} = 50$$ and standard deviation $$s = 5$$?

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

Question 1

Which of the following best describes the concept of variation in a data set?

Accepted Answer

The amount of fluctuation or spread of the observations around their mean.

Question 2

Given the data set: 10, 60, 50, 30, 40, 20, what is the range?

Accepted Answer

$$	ext{Range} = 60 - 10 = 50$$

Question 3

Which formula is used to calculate the population variance?

Accepted Answer

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

Question 4

Why is the sample variance divided by $$(n-1)$$ instead of $$n$$?

Accepted Answer

To make the sample variance an unbiased estimator of the population variance.

Question 5

A data set has a mean of 100 and a standard deviation of 15. According to the empirical rule, approximately what percentage of data falls between 85 and 115?

Accepted Answer

About 68%

Question 6

If a value in a data set has a z-score of $$-2.5$$, how would you interpret this value?

Accepted Answer

It is significantly low.

Question 7

Given a sample: 11, 90, 33, 49, 27, what is the sample mean?

Accepted Answer

$$\bar{X} = \frac{11 + 90 + 33 + 49 + 27}{5} = 42$$

Question 8

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is resistant to outliers.

Question 9

A student scored 65 on a calculus test (mean = 50, standard deviation = 10) and 30 on a history test (mean = 25, standard deviation = 5). What is the student’s z-score for the calculus test?

Accepted Answer

$$z = \frac{65 - 50}{10} = 1.5$$

Question 10

Which of the following values would be considered an outlier using the IQR method if $$Q1 = 20$$, $$Q3 = 40$$, and $$IQR = 20$$?

Accepted Answer

A value of 10

Question 11

What is the coefficient of variation (CV) for a sample with mean $$\bar{X} = 50$$ and standard deviation $$s = 5$$?

Accepted Answer

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

Question 12

Using Chebyshev’s Theorem, what is the minimum proportion of data that must lie within 3 standard deviations of the mean for any data set?

Accepted Answer

At least $$\frac{8}{9} or $$about 89%

Question 13

Which of the following is the correct formula for a z-score in a population?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 14

A boxplot is constructed using which of the following values?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 15

If the mean price of condos is $$50,000 with a standard deviation of 10$$,000, what is the price range for which at least 75% of condos will sell according to Chebyshev’s Theorem?

Accepted Answer

$$30,000 to$$ $$70,000$$

Question 16

Which of the following statements about percentiles is TRUE?

Accepted Answer

Percentiles divide a data set into 100 groups with about 1% of the values in each group.

Question 17

Which value is NOT included in the five-number summary?

Accepted Answer

Mean

Question 18

If a newborn baby’s head circumference is 16 inches, and the mean is 12 inches with a standard deviation of 0.5 inches, is this value significantly high according to the range rule of thumb?

Accepted Answer

Yes, because it is greater than $$13$$ inches ($$12 + 2 	imes 0.5)$$

Question 19

Which of the following is a property of the sample variance?

Accepted Answer

It is always positive.

Measures of Variation and Relative Standing in Statistics

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