standard error question

I am having problems getting started on problem

If I have a data set of 300 and the standard deviation is 20,000, how much smaller will the standard deviation be if I have a data set of 1,000?

I'm lost on where to begin

thanks

You do not have a proper understanding. The population has a standard deviation. There is nothing you can do about it.

If we ask a better question, we might be able to make up an answer.

Given a population with unknown standard deviation and unknown mean, we are attempting to estimate the mean. A sample of 300 produced a sample mean (the we don't care about at thte moment) with a sample standard deviation of the mean of 20,000. What would be the sample standard deviation of the mean if we increased the sample size to 1,000?

\(\displaystyle 20000 = \frac{Something}{\sqrt{300}}\)

Now what?

I think what I am asking is (i) if I increase the sample population size from 300 to 1000 will the mean change and (ii) is there a way to quantify how much lower the SD will be.
Thanks

You do not have a proper understanding. The population has a mean. There is nothing you can do about it. Why would the mean change if you picked a larger sample. Would you expet the Sample Mean to change?

\(\displaystyle 20000 = \frac{Something}{\sqrt{300}} \implies\) What?

Maybe, \(\displaystyle \frac{Something}{\sqrt{1000}} = \frac{Something}{\sqrt{1000}}\cdot\frac{\sqrt{300}}{\sqrt{300}} = \frac{Something}{\sqrt{300}}\cdot\frac{\sqrt{300}}{\sqrt{1000}} = 20000\cdot\frac{\sqrt{300}}{\sqrt{1000}}\)

Are we getting anywhere?

Thank you for your help.
I appreciate that a population has an inherent mean but ...let's say that the population has 1M data points and we get a sample of this population that contains a 100 points, and a sample that contains 10,000 points. Wouldn't the larger sample have a mean that better approximates the population mean?

The larger sample would have a smaller standard deviation around it's mean estimate.

right, but would the mean change?

The expected value of an unbiased estimator of the mean is the mean of the underlying distribution. The sample mean will change with a different sample, whether smaller or larger, but this is only a function of the sample. If you take another sample of the same size, you will get a different sample mean (unless something weird happens). There is nothing about a sample size that says "This is the real mean of the population", well, until your sample is the entire population, but that's not really a sample, is it? The goal of a larger sample size is the decrease in the variance.

Eureka ...I think that I get it!!...sorry, I have a hard time visualizing these concepts.

Thank you very much for taking the time to explain it to me.