A statistic estimates a parameter
The sample mean is the observed sum divided by the sample size. It estimates the population mean, which generally cannot be measured by surveying everyone.
Probability & statistics / English
Sample variance | Descriptive statistics | Probability and Statistics | Khan Academy
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Estimate a population mean and variance from a sample, and distinguish variance formulas with divisors n and .
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1:30A statistic estimates a parameter6:00The same squared-deviation total9:00Why use ?Learning script
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The sample mean is the observed sum divided by the sample size. It estimates the population mean, which generally cannot be measured by surveying everyone.
For the six observations here, the mean is 2 and the squared deviations sum to 6.5. Dividing by n gives about 1.08, while dividing by gives 1.3.
For iid observations with finite variance and , dividing by makes the sample variance unbiased for population variance. This corrects the average downward bias from estimating the mean in the same sample.
Knowledge cards
The same squared-deviation total
For the six observations here, the mean is 2 and the squared deviations sum to 6.5. Dividing by n gives about 1.08, while dividing by gives 1.3.
Why use ?
For iid observations with finite variance and , dividing by makes the sample variance unbiased for population variance. This corrects the average downward bias from estimating the mean in the same sample.
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- Variance ExplanationAt 1:30
Why this connection?
The sample mean is the observed sum divided by the sample size. It estimates the population mean, which generally cannot be measured by surveying everyone. For the six observations here, the mean is 2 and the squared deviations sum to 6.5. Dividing by n gives about 1.08, while dividing by gives 1.3. For iid observations with finite variance and , dividing by makes the sample variance unbiased for population variance. This corrects the average downward bias from estimating the mean in the same sample.
Questions this video answers
Understand why↗
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.
Find a method↗
To estimate the population mean from a sample, you calculate the sample mean by dividing the observed sum of the sample values by the sample size. This sample mean serves as the point estimate for the population mean, which generally cannot be measured directly by surveying everyone.
Conditions: You have a sample of observations.; The population mean is the target parameter to estimate.
Find a method↗
To compute the sample variance using the divisor n, you first calculate the mean of the sample. Then, you find the sum of the squared deviations of each observation from this sample mean.
Conditions: You have a sample of observations.; You are calculating the variance with divisor n.
Find a method↗
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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