Statistics Question: How is the Estimation Theory related to Variance and Standard Deviation?

Statistics Question: How is the Estimation Theory related to Variance and Standard Deviation?

Statistics Question: How is the Estimation Theory related to Variance and Standard Deviation?
When we want to estimate some quantity (for example, the distribution mean) from random data, we are often very concerned with the accuracy and statistical significance of our estimate. For example, we may want a Minimum Variance Unbiased (MVU) estimator.





To put it another way, when we estimate something based on random data, the estimator is another random variable. How do we characterize random variables? The variance (or standard deviation) is one important characteristic. It tells us how much scatter to expect.





For example, if we want to estimate the average age of people who see a particular movie in theaters, we could sample the distribution by conducting a poll at a few theaters. If there is a lot of variation in the averages between theaters, that tells us that there is a lot of uncertainty in our estimate.

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