Question 1

Which of the following best describes why the range is not a resistant measure of variation?

Accepted Answer

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

Question 2

Given a data set with a mean of $$\mu = 12$$ ounces and a standard deviation of $$\sigma = 0.5$$ ounces, according to the range rule of thumb, what is the approximate range of 'not significant' values?

Accepted Answer

$$10.5 to$$ $$13.5$$ ounces

Question 3

Which property is true for the standard deviation $$s of a $$sample?

Accepted Answer

It is zero only when all data values are exactly the same.

Question 4

Suppose you have two data sets: one with a standard deviation of $$0.1$$ and another with a standard deviation of $$1.5. $$What does this indicate about the variation in the two data sets?

Accepted Answer

The second data set has greater variation.

Question 5

If the sample standard deviation $$s is a $$biased estimator of the population standard deviation $$\sigma$$, what does this mean?

Accepted Answer

Sample values of $$s$$ tend to be systematically higher or lower than $$\sigma.$$

Question 6

According to the Empirical Rule, approximately what percentage of data falls within 2 standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

$$95\%$$

Question 7

Chebyshev's Theorem states that for any data set, at least what proportion of values lie within $$K=3$$ standard deviations of the mean?

Accepted Answer

$$89\%$$

Question 8

Given the two histograms in the image, which cola (Regular or Special) likely has a larger standard deviation?

Accepted Answer

Special Cola

Question 9

If a data set has a mean of $$\mu = 10$$ and a standard deviation of $$\sigma = 2$$, what is the variance $$\$$sigma^2$$?

Accepted Answer

$$4$$

Question 10

A sample of cola volumes has a minimum value of $$11.8$$ ounces and a maximum value of $$12.6$$ ounces. What is the range?

Accepted Answer

$$0.8$$ ounces

Question 11

A data set has a mean of $$\mu = 15$$ and a standard deviation of $$\sigma = 3. $$According to the Empirical Rule, what is the interval that contains about $$68\% of $$the data?

Accepted Answer

$$[12, 18]$$

Question 12

Which of the following statements is true about the units of standard deviation?

Accepted Answer

They are the same as the units of the original data.

Question 13

If a data set contains an outlier, which measure of variation is most likely to be affected?

Accepted Answer

Standard deviation

Question 14

A researcher claims that at least $$75\% of $$all values in any data set must lie within 2 standard deviations of the mean. Which theorem supports this claim?

Accepted Answer

Chebyshev's Theorem

Question 15

If the sample variance $$s^2 = 2.25$, what is the sample standard deviation s$?

Accepted Answer

$$1.5$$

Measures of Variation in Statistics: Range, Standard Deviation, Variance, and Related Rules

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