How do you compute the sample variance using the divisor n?
Conditions
- You have a sample of observations.
- You are calculating the variance with divisor n.
Reasoning, step by step
- Calculate the sample mean.
- Compute the squared deviation of each observation from the sample mean.
- Sum all the squared deviations.
- Divide the sum of squared deviations by the sample size n.
Example
For the six observations here, the mean is 2 and the squared deviations sum to 6.5. Dividing by n gives about 1.08.
Common misconceptions
- Forgetting to square the deviations before summing them.
- Dividing by n-1 instead of n when specifically asked for the divisor n calculation.
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For iid observations with finite variance and , dividing by n-1 makes the sample variance an unbiased estimator for the population variance. This correction addresses the average downward bias that occurs when estimating the mean in the same sample used to calculate the variance.
Conditions: The observations are independent and identically distributed (iid).; The population has finite variance.; The sample size n is greater than 1.
To compute the sample variance using the divisor n-1, you calculate the sum of the squared deviations of each observation from the sample mean. Then, you divide this squared-deviation total by n-1, where n is the sample size.
Conditions: You have a sample of observations.; You are calculating the variance with divisor n-1.
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