Math Is Fun Forum

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Standard Error or Standard Deviation ?

Hello,

May I know the difference between standard deviation and standard error?

Many thanks

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Only a friend tells you your face is dirty.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Standard Error or Standard Deviation ?

hi math9maniac

If you know all the values in a population (say height of people) then you can calculate the standard deviation as a measure of spread.  It's the square root of the deviations from the mean squared.

But often it wouldn't be practical to get every value so it is necessary to investigate a sample and estimate the sd. from those values.

Let's say you have a sample of size n.  If you could take sample after sample and get the mean of each sample, these means would themselves form a distribution with a mean and sd.  It can be shown that the mean of these sample means is likely to be the mean of the real population (more samples means a better estimate of this) and the sd (s) of the sample means is the standard error.  Using the formula

where s is the standard error and sigma is the population sd, you can then estimate the population sd.

There is a wiki page on this here:

https://en.m.wikipedia.org/wiki/Standard_error

There is also some notes on this here:

https://www.mathsisfun.com/data/standar … mulas.html

but the proof is not given there.

I'm a bit rusty on this but could look it up if you want.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob