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I am currently taking a statistics class where we are studying about Standard Deviation. Even though it is a new concept for me still I am able to grasp it fairly quickly. But, we discussed something in the class which I could not understand.

The ±2 SD covers 95% of the data set. But when analyzing some data, what are some of the implications of ±2 SD? What I can tell is that you are missing out the 5% of the remaining data that can give you more accurate information about the data as a whole, like the range of the data, etc. But please please let me know if anyone has more implications of ±2 SD.

Aiguo
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    This is not clear. It is not generally true that $\pm 2 \sigma$ around the mean covers $95%$ of the data. This is true for Normally Distributed data, but not all data is normally distributed. And, to stress, you never said anything about the distribution you had in mind. In general, you have Chebyshev's Inequality. – lulu Feb 07 '19 at 18:25
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    Your question isn't quite specific enough to answer substantively. Keep in mind that the 95 percent rule only applies, strictly speaking, to normal distributions. In general, the coverage of $\pm 2 \sigma$ could embrace up to 100 percent, or as low as 75 percent. See the Wikipedia plot summary on Chebyshev's inequality for more details on this. – Brian Tung Feb 07 '19 at 18:26
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    Holy cow, @lulu. Get out of my head. :-) – Brian Tung Feb 07 '19 at 18:27
  • @BrianTung Those comments are really amazingly similar. – lulu Feb 07 '19 at 18:28

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