Sample Size and Standart error

You record your sleeping for 1 year lets say.
And you find average to be 10 hours.(This is average of all individual days)

And you find population standard deviation as 2.

Leftmost part in picture.

You randomly take 10 days within a year and take average.
Repeat this process for lots of time to take average of different "10 samples" .
*** Be careful you now took average of only a sample subset.

Middle part in picture.

Standard error is = 2 / √ 10 
Standard error = 0.63
This value means with 10 samples we are 0.63 far from real mean which is 10.

You can see that sample graph


If we get 100 samples it is more centered around real mean.
Standard error is = 2 / √ 100 
Standard error = 0.2


More samples the more you are near to Population mean.

Standard error = Standard Deviation / SQRT( Sample Size)

So if Standard deviation is high, (your data varies a lot ) , you will have big error for samples.