A little confused here,

- the standard Deviation of the single population is always HIGHER than Standard Error (Standard Deviation) of Sample mean.
- 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.