• • • ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™ CX
TI-Nspire™ CX CAS

5.0

# Statistics: Why Divide by n-1?

by Texas Instruments

#### Objectives

• Students will recognize that the mean of all the sample variances for samples of a given size drawn with replacement calculated using n-1 as a divisor will give the population variance calculated using n as a divisor.
• Students will recognize that the mean of all the sample variances for samples of a given size drawn without replacement calculated using n-1 as a divisor will give a value equal to the population variance if calculated using n-1 as a divisor.
• Students will recognize that as the sample size increases the difference in calculating the variances for a sample using n and n-1 as a divisor will decrease.
• Students will recognize that when a sample variance is calculated using n-1 as a divisor, the sample variance produces an unbiased estimator of the population variance.

#### Vocabulary

• bias
• mean
• parameter
• population
• sample size
• sampling distribution
• standard deviation
• variance