Question 1

Which of the following best describes the range of a data set?

Accepted Answer

The difference between the maximum and minimum data values.

Question 2

Why is the range considered a non-resistant measure of variation?

Accepted Answer

It only uses the maximum and minimum values, making it sensitive to extreme values.

Question 3

Given the following wait times (in minutes): 50, 25, 75, 35, 50, 25, 30, 50, 45, 25, 20, what is the range?

Accepted Answer

$$55.0$$

Question 4

Which formula is used to calculate the sample standard deviation?

Accepted Answer

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

Question 5

What does a larger value of the sample standard deviation $$s$$ indicate?

Accepted Answer

Greater amounts of variation among the data values.

Question 6

Why do we divide by $$(n-1)$$ instead of $$n$$ when calculating the sample variance?

Accepted Answer

To ensure the sample variance is an unbiased estimator of the population variance.

Question 7

Using the shortcut formula, which equation correctly calculates the sample standard deviation for a data set?

Accepted Answer

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

Question 8

According to the empirical rule, what percentage of data values fall within 2 standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

$$95\%$$

Question 9

Chebyshev’s theorem states that for any data set, at least what proportion of values lie within 3 standard deviations of the mean?

Accepted Answer

$$\frac{8}{9}$$

Question 10

If a sample has a mean of $$100$$ and a standard deviation of $$15$$, what is the coefficient of variation?

Accepted Answer

$$15\%$$

Question 11

Which of the following is true about the units of variance?

Accepted Answer

The units of variance are the squares of the units of the original data values.

Question 12

A sample of 11 wait times has a range of $$55$$ minutes. Using the range rule of thumb, estimate the standard deviation.

Accepted Answer

$$13.75$$ minutes

Question 13

Which of the following statements is correct regarding biased and unbiased estimators?

Accepted Answer

The sample standard deviation $$s is a $$biased estimator of the population standard deviation $$\sigma.$$

Question 14

If a data set is approximately bell-shaped, what percentage of values fall within 1 standard deviation of the mean according to the empirical rule?

Accepted Answer

$$68\%$$

Question 15

Which formula is used to calculate the population standard deviation?

Accepted Answer

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

Question 16

A sample has a mean of $$50$$ and a standard deviation of $$10. $$What is the coefficient of variation?

Accepted Answer

$$20\%$$

Question 17

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

Accepted Answer

It is always negative.

Question 18

If the sample mean is $$39.1$$ and the sum of squared deviations is $$2740.91$$ for a sample of $$11$$ values, what is the sample standard deviation?

Accepted Answer

$$16.6$$

Question 19

Which of the following best describes the coefficient of variation?

Accepted Answer

It is the ratio of the standard deviation to the mean, expressed as a percentage.

Question 20

According to Chebyshev’s theorem, what is the minimum percentage of values that must lie within 2 standard deviations of the mean for any data set?

Accepted Answer

$$75\%$$

Measures of Variation in Descriptive Statistics

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