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Again: this is not a GMAT type of question, plus it has very poor and ambiguous wording. So, I wouldn't worry about it at all.

Anyway: you won't be asked to actually calculate the standard deviation of a set on the GMAT. You just need to understand the concept of it: standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

How many integers lie between the mean and the Standard deviation?

Given 25,30,35,40,45.

This is not a GMAT type of question plus it has very poor and ambiguous wording.

If the question is: how many of the 5 listed data points are within 1 standard deviation of the mean then the answer will be 3: mean=35 and SD=~7, so there are 3 data points from mean-SD=35-7=28 to mean+SD=35+7=42, namely: 30, 35, and 40. _________________

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