If nothing is known about the shape of the distribution of a quantitative variable, what percentage of data fall within 2 standard deviation of the mean?

At least 75% of the data will fall within 2 standard deviations of the mean. This is tricky problem. Usually when you're dealing with standard deviation, you have a bell curve, or something close to a bell curve and for such a data distribution, there will be approximately 95% of the data within 2 standard deviations of the mean. But if you don't know that you have a bell curve, you have to fall back to Chebyshev’s Theorem, which states that at least 75% of the data points will fall within 2 standard deviations of the mean for any set of numbers.

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