Exploring Measures of Dispersion: Range, Variance, and Standard Deviation

What is the arithmetic mean of the data set: -10, 0, 10, 20, 30?

• 0

• 10

• 20

• 30

Which of the following data sets has the same arithmetic mean as the set: -10, 0, 10, 20, 30?

• 8, 9, 10, 11, 12

• 0, 5, 10, 15, 20

• 5, 10, 15, 20, 25

• 1, 2, 3, 4, 5

What is the range of the data set: -10, 0, 10, 20, 30?

• 20

• 30

• 50

• 40

Why might range not always be a reliable measure of dispersion?

• It is the same as variance

• It can be affected by outliers

• It only considers the mean

• It is difficult to calculate

What is the symbol for population variance?

• π

• μ

• σ

• σ²

How is variance calculated?

• Sum of data points divided by number of points

• Square root of the mean

• Difference between maximum and minimum values

• Average of squared differences from the mean

What is the variance of the data set: -10, 0, 10, 20, 30?

• 300

• 200

• 100

• 400

What is the standard deviation of a data set if its variance is 200?

• 10√2

• 20

• 14.14

• 10

What is the relationship between variance and standard deviation?

• Variance is the square of standard deviation

• Standard deviation is the square root of variance

• They are unrelated

• Variance is always larger than standard deviation

Which data set has a higher standard deviation: -10, 0, 10, 20, 30 or 8, 9, 10, 11, 12?

• 8, 9, 10, 11, 12

• Cannot be determined

• -10, 0, 10, 20, 30

• Both have the same