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Chebycheves rule

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Step 1

Chebyshev’s rule:

The proportion of any distribution that lies within k standard deviations of the mean is at least 1 – 1/k^2

Where k is any positive number greater than 1.

This rule is applying to all distributions of the data.

So, for example, this rule says that within two standard deviations of the mean, you will find at least

1 – 1/k^2  = 1 – (1 / 2^2) = 1 – ¼ = ¾

= 0.75 , or at least 75%

Step 2

We will take one example for better understanding,

Suppose that the average score on a math test is a 84 with standard deviation of 4 points. According to Chebyshev’s rule, at least what percent of the tests have a grade of at lease 72 and at most 96?

Step 3

Here, we can see standard deviation is σ = 4, So in this...

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