# Simulation providing evidence that (n-1) gives us unbiased estimate | Khan Academy | Summary and Q&A

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November 26, 2012
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Simulation providing evidence that (n-1) gives us unbiased estimate | Khan Academy

## TL;DR

This simulation explains why we divide by n-1 when calculating sample variance, giving an unbiased estimate of population variance.

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### Q: What does the simulation allow users to do?

The simulation allows users to construct a population distribution, calculate its parameters, and take samples of different sizes.

### Q: How does the simulation calculate the variance for each sample?

The simulation calculates the variance by subtracting the sample mean from each data point, squaring the result, and dividing it by n plus a (where a varies from n-3 to n+a).

### Q: What happens when users generate multiple samples and average their variances?

When multiple samples are generated and their variances are averaged, it becomes clear that dividing by n-1 gives the best estimate for population variance.

### Q: Why is dividing by n-1 important in calculating sample variance?

Dividing by n-1, instead of n, accounts for the degrees of freedom in the sample and provides an unbiased estimate of population variance.

## Summary & Key Takeaways

• The simulation allows users to construct a population distribution and calculate its parameters, such as mean and standard deviation.

• Users can then take samples of different sizes and calculate the variances.

• Through the simulation, it becomes evident that dividing by n-1 gives the best estimate for population variance.