Standard Deviation and Standard Error are often confused with one another. Let’s clear that up once and for all.

Standard Deviation, as you might know, describes or quantifies the variation in the data on both the sides of the distribution - lower than mean and greater than mean. If your data points are spread across a large range of values, the standard deviation will be high.

Now, as I already described in my previous posts, by Central Limit Theorem, if we plot the means of all the samples from a population, the distribution of those means will again be a normal distribution. So it will have its own standard deviation, right?

The standard deviation of the means of all samples from a population is called as Standard Error. The value of Standard Error will be usually less than the Standard Deviation as you are calculating standard deviation of means, and value of means would be less spread than individual data points due to aggregation.

You can even calculate standard deviation of medians, mode or even standard deviation of standard deviations!

#statistics #datascience #machinelearning