Suppose that someone was collecting samples and he was trying to estimate the average amount of money people spend on purchasing fast food meals. The calculated mean was USD 50 and the standard deviation was USD 7.
This doesn't tell us enough information. But that is ok, we can tease out the likely answer.
So, our problem is decoding the calculated mean of what was USD 50? Was it some sampling of people spending money on fast food meals? Or, was it every single fast food meal purchased?
In the first case, 50 USD is the sample mean. They checked 10 people, and the average spend was 50 USD.
In the second case, 50 USD is the population mean. They checked every person, and the average spend was 50 USD.
Now, the SD probably means the standard deviation of the points that are averaged. But in the first case, statisticians sometimes get fancy, and attempt to calculate the distribution of the actual population mean given the sampling data gathered. Those statisticians, trying to produce useful information.
Here, 50 USD is the mean of the estimate of the population mean, and 7 USD is the standard deviation on the population mean given the sample data.
- Does SD show that, on average, people spend between USD 43 and USD 57 on meals?
If 50 is the population mean, and the SD is 7, then we are pretty certain that a good percentage of the population spends between USD 43 and 57 on meals; that is 1 SD away from the mean. As it is almost certain that the distribution of meal purchases is going to be somewhat normal, this is a safe bet.
- Or, on average, they spend USD 50 per purchase but their purchase amount has a relatively large standard deviation of USD 7?
This again is a population mean of 50 USD. It is another way to say the previous point, with more precision and less assumptions.
- Or, on average, they spend USD 50 per purchase but my estimate has a relatively large standard deviation of USD 7?
This is a case where we read the USD 50 as an estimate of the population mean.
Which of these is in play is not actually described well by the question.
But based on the test taking strategy (first two answers are variations on each other) and the fact that the initial paragraph talked about estimating the average, the difficulty of actually getting data for the entire population, and the fact that statisticians do this operation a lot, I'd go with this one.
Now, statisticians attempt to estimate the actual average based on the sample data; but in doing so, they make assumptions about the underlying distribution (quite reasonable ones). As an example of how you might do this, you might use Student's T distribution, which assumes a-priori that the purchases made are normal, but with unknown mean and standard deviation.
Then from a set of samples, you can generate an estimate of the population mean and a standard deviation of the error in your estimate.
I'm guessing this is what the situation is being described.