Question 1

Which of the following best describes the main difference between variance and standard deviation?

Accepted Answer

Variance measures the average squared deviation from the mean, while standard deviation is the square root of the variance.

Question 2

Given a data set with values measured in meters, what are the units of its variance and standard deviation?

Accepted Answer

Variance: meters squared; Standard deviation: meters

Question 3

Suppose you have a data set: 2, 4, 6, 8. What is the variance of this data set?

Accepted Answer

$$ \frac{20}{3} \approx 6.67 $$

Question 4

Why does variance use squared deviations rather than absolute deviations?

Accepted Answer

Because squaring emphasizes larger deviations (outliers) more than smaller ones.

Question 5

Which formula correctly represents the variance of a population?

Accepted Answer

$$ S^2$ = \frac{\sum (x - M)^2$}{n} $$

Question 6

A financial analyst is comparing the risk of two investment portfolios. Which statistical measure should they use to compare the average squared deviation of returns from the mean?

Accepted Answer

Variance

Question 7

If the variance of a data set is 25, what is the standard deviation?

Accepted Answer

$$ 5 $$

Question 8

Which of the following statements is TRUE regarding the interpretation of standard deviation?

Accepted Answer

Standard deviation is in the same units as the original data.

Question 9

A pharmaceutical company is analyzing the consistency of pill weights produced by a machine. Which measure would best indicate the absolute variability in pill weights?

Accepted Answer

Standard deviation

Question 10

If all values in a data set are increased by a constant, how does this affect the variance and standard deviation?

Accepted Answer

Both variance and standard deviation remain unchanged.

Question 11

Which of the following real-world scenarios would most likely require the use of standard deviation rather than variance for interpretation?

Accepted Answer

Reporting the typical daily temperature fluctuation in degrees Celsius.

Question 12

Given the formula for standard deviation $$ S = \sqrt{\frac{\sum (x - M)^2$}{n}} $$, what is the effect of an outlier on the value of $$ S $$?

Accepted Answer

It increases $$ S $$ significantly because the squared deviation of the outlier is large.

Question 13

A researcher finds that the variance of test scores in a class is 16. What is the standard deviation, and what are its units if the test scores are in points?

Accepted Answer

$$ 4 $$ points

Question 14

Which of the following is NOT a correct property of variance?

Accepted Answer

Variance is always negative.

Question 15

If the standard deviation of a data set is zero, what can you conclude about the data?

Accepted Answer

All values in the data set are identical.

Variance and Standard Deviation: Definitions, Differences, and Applications

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