Given a normal distribution of data, we know from the Empirical Rule that in between 2 standard deviations from the mean(i.e. xbar – 2s..to..xbar + 2s) there lies about 95% of all the data.

Calculate and show the percentage of data from xbar – 2s..to..xbar + 2s using Chebyshev’s theorem.

Now, if I told you that a certain data set has about 87% of the data between the data points xbar + 2s, how would you reconcile this percentage against what is known for both the Empirical Rule and what you calculated above with Chebyshev’s theorem?

Please see the attached file.

Statistics, All Topics

Year 3

Normal distribution of data

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Given a normal distribution of data, we know from the Empirical Rule

that in between 2 standard deviations from the mean (i.e. xbar –

2s..to..xbar + 2s) …

The solution gives a comparison of empirical rule and Chebyshev’s theorem for normal distribution.