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In the sampling distribution of the sample means, the standard error of the mean will vary...

In the sampling distribution of the sample means, the standard error of the mean will vary according to the size of the sample. As the sample size, n, gets larger, the dispersion of the sampling distribution of the means gets larger.

Math   Statistics-And-Probability   
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Answer #1

The dispersion of sampling distribution is  which is the standard deviation or standard error.

Hence as the sample size increase dispersion will ne smaller.

Pleasr note,

The formula of standard deviation of the sampling distribution of sample mean is when population standard deviation is and the sample points are independent.

But if they're not independent then also it will be inversely proportional to the sample size.

Hence increase in sample size makes dispersion smaller.

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