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Thorem stating how much of a population is within n standard deviations from the mean

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2 In a statistics class I took in college, I remember learning about a theorem stating that 50% of the population must be within 1σ from μ, 75% within 1σ, and so on, regardless of the distribution. The distribution can be tighter, but this much is a guarantee. People don't seem to be familiar with this, I'm not sure I remembered the numbers right, and I'm not sure this even exists. Is this a thing? probability-distributions standard-deviation share | cite | improve this question asked 1 hour ago David Ehrmann 111 2 New contributor