# Sampling topics CFA level 1

A little confused here,

1. the standard Deviation of the single population is always HIGHER than Standard Error (Standard Deviation) of Sample mean.
2. Sampling size increased, the the Standard Error of Sample mean will fall (According to the properties of point estimators)

So why is that as Sampling size increased (approaching to actual population number) , the smaller the Standard Error (Standard Deviation) of Sample mean will be ? Shouldn’t it be higher to approach the standard Deviation of Population.

Examples let say, The population is 100 which Standard Deviation of Population is 10 and Standard Error (Standard Deviation) of Sample mean is 7 with 50 samples.

As we increased sample size to let say 99 , shouldn’t the Standard Error (Standard Deviation) of Sample mean increase ?
And what exactly Standard Error (Standard Deviation) of Sample mean is ?

Hope this will be clarified, thank you so much.

I just realised that Standard Deviation of Sample mean vs Standard deviation of sample are 2 different meaning ?? Could please explain the meaning of this 2 ? Much appreciated !

standard error of a sample will always be smaller than the standard deviation of the population because. the standard error = standard deviation / squareroot (sample size).

Standard error will fall as sample size gets bigger because once you have more data points, your distribution becomes more normal. And also think of the denominator I pointed out in the first paragraph. But let’s think about it logically. If you have a small sample size, say 10, you will have a lot of variance in your data. But if you have a huge sample size, say 1,000 then your variance will be smaller. Does that make sense?

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First, there is no such thing as the “standard error of a sample”. I believe that you meant the standard error of the sample mean.

Second, the standard error of the sample mean will not always be less than the standard deviation of the population: suppose that the sample size is 1.