Standard deviation versus standard error

A topic which many students of statistics find difficult is the difference between a standard deviation and a standard error.

The standard deviation is a measure of the variability of a random variable. For example, if we collect some data on incomes from a sample of 100 individuals, the sample standard deviation is an estimate of how much variability there is in incomes between individuals. Let's suppose the average (mean) income in the sample is $100,000, and the (sample) standard deviation is $10,000. The standard deviation of $10,000 gives us an indication of how much, on average, incomes deviate from the mean of $100,000.

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