Range, Variance, Standard Deviation, Coefficient of Variation, Chebyshev’s Theorem, Empirical Rule (Normal)

What is the formula to calculate the range of a data set?

• Range = Maximum Value * Minimum Value

• Range = Maximum Value + Minimum Value

• Range = Maximum Value / Minimum Value

• Range = Maximum Value - Minimum Value

How is variance calculated for a given data set?

• Variance is calculated by finding the median of the squared differences between each data point and the median of the data set.

• Variance is calculated by summing all the data points in the set.

• Variance is calculated by finding the mean of the squared differences between each data point and the mean of the data set.

• Variance is calculated by dividing the sum of the data points by the number of data points.

What does the standard deviation measure in a data set?

• Mean of the data set

• Amount of variation or dispersion from the mean

• Median of the data set

• Number of data points

How is the Coefficient of Variation (CV) calculated?

• CV = (Mean / Standard Deviation) * 100

• CV = (Standard Deviation / Mean) * 100

• CV = (Mean + Standard Deviation) * 100

• CV = (Standard Deviation - Mean) * 100

What is Chebyshev’s Theorem used for in statistics?

• Chebyshev’s Theorem is used to calculate the mean of a data set

• Chebyshev’s Theorem is used to determine the mode of a data set

• Chebyshev’s Theorem is used to determine the proportion of any data set that must lie within a certain number of standard deviations from the mean, regardless of the shape of the distribution.

• Chebyshev’s Theorem is used to predict future trends in data analysis

What percentage of data falls within one standard deviation of the mean in a normal distribution according to the Empirical Rule?

• 50%

• 68%

• 75%

• 90%

In a normal distribution, what percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

• 90%

• 99%

• 85%

• 95%

What is the range of a data set with values {10, 15, 20, 25, 30}?

• 5

• 35

• 18

• 20

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

• 10

• 20

• 15

• 5

If the mean of a data set is 50 and the standard deviation is 10, what is the Coefficient of Variation?

• 30%

• 20%

• 25%

• 15%