How good this estimate is depends on the shape of the original distribution of sampling units (the closer to normal the better) and on the sample size (the larger the sample the better).
This estimate is derived by dividing the standard deviation by the square root of the sample size. In lieu of taking many samples one can estimate the standard error from a single sample. The standard deviation of this set of mean values is the standard error. We calculate the mean of each of these samples and now have a sample (usually called a sampling distribution) of means. Let’s say that instead of taking just one sample of 10 plant heights from a population of plant heights we take 100 separate samples of 10 plant heights. The standard error, on the other hand, is a measure of the variability of a set of means. The 5 cm can be thought of as a measure of the average of each individual plant height from the mean of the plant heights. We can say that our sample has a mean height of 10 cm and a standard deviation of 5 cm. Let’s say we have a sample of 10 plant heights. The standard deviation is a measure of the variability of a single sample of observations. What is the difference between STANDARD DEVIATION and STANDARD ERROR?
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