3.2 Measures of Spread

Question 1

Range

Answer 1

Largest minus Smallest

Question 2

Population Variance

Answer 2

Square of the polulation standard deviation.

Question 3

Sample Variance

Answer 3

Square of the sample standard deviation.

Question 4

Sample Standard Deviation

Answer 4

Measures the average distance the data values deviate from the mean. Represented by the symbol “S”.

Question 5

Population Standard Deviation

Answer 5

Measures the average distance the data values deviate from the mean. Represented by the symbol “σ”.

Question 6

Empirical Rule

Answer 6

When a population is approximately bell shaped, approximately 68% of the population will be within 1 standard deviation from the mean. Approximately 95% will be within 2 standard deviations of the mean. Almost all of the data will be within 3 standard deviations of the mean.

Question 7

Chebyshev’s Inequality

Answer 7

In any data set, the proportion of the data that will be within k standard deviations of the mean is at least: 1-(1/k²).

Question 8

Coefficient of Variation

Answer 8

Found by dividing the standard deviation by the mean.

CV = σ/µ