What does standard deviation mean in this case? 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. I want to know the right meaning of standard deviation from the below answers because I understand the definition but I don't know how this can be applied or what is the benefit of SD in real life.

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*Does SD show that, on average, people spend between USD 43 and USD 57 on meals?

*Or, on average, they spend USD 50 per purchase but their purchase amount has a relatively large standard deviation of USD 7?

*Or, on average, they spend USD 50 per purchase but my estimate has a relatively large standard deviation of USD 7?


I'm surprised no one answered with the rule-of-thumb for regarding the standard deviation in data with normal distributions:  The 68-95-99.7 rule.  (See Wikipedia article.
If you have normally-distributed data, about 68% of observations fall within the range of  the mean ± the standard deviation. And about 95% of observations fall within the mean ± two standard deviations.
As far as I can tell, for a uniform distribution, about 58% of observations fall within μ ± σ, and 100% fall within μ ± 2σ.
It appears that for skewed distributions, more of the data would fall within μ ± σ, so that for a common log-normal distribution, perhaps 75% of observations fall within μ ± σ.
The data could also have a bimodal distribution.  For a pretty obviously bimodal distribution, perhaps more that 50% of observations fall within μ ± σ.
EDIT:  To make these observations more explicitly tied to the question:  It depends on the distribution of the data, and on what you mean by "on average", but probably more than 50% of observations fall within μ ± σ , so "on average, people spend between USD 43 and USD 57 on meals" isn't a bad interpretation of the statistics presented.
EDIT 2: I bolded the mentioned distributions to make the logic of my answer more apparent.
