Standard Error

00:01 In the previous lesson, we show that no matter the underlying distribution of the data set, distribution of the sample means would be normal with a mean equal to the original mean and a variance equal to the original variance divided by the sample size. All right.

00:17 This lecture will be very short and has the sole purpose of defining what a standard error is. The standard error is the standard deviation of the distribution form by the sample means.

00:29 In other words, the standard deviation of the sampling distribution.

00:33 So how do we find it? We know it's variance sigma squared divided by n.

00:39 Therefore, the standard deviation is sigma divided by the square root of n.

00:45 Done like a standard deviation.

00:48 The standard error shows variability.

00:50 In this case, it is the variability of the means of the different samples we extracted.

00:58 You can guess that since the term has its own name, it is widely used and very important. Why is it important? Well, it is used for almost all statistical tests because it shows how well you approximated the true mean.

01:11 More on that in the next lessons.

01:14 Note that it decreases as the sample size increases.

01:18 This makes sense as bigger samples give a better approximation of the population.

01:23 That's all for now.

01:25 Thanks for watching.