What is the empirical rule? How is it useful?

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Expert Solution

The empirical rule tells that for a normal distribution, all the data (nearly) will be falling within 3 standard deviation of the mean which can also be stated as 68% of the data will fall within first standard deviation of the mean or 95% will fall within two standard deviation of the mean or 99.7% of the data will fall within 3 standard deviation of the mean.

The empirical rule is useful in below cases:

1.You can use the empirical rule to determine if your data follows a normal distribution or not.

2.If you're given the mean and standard deviation of a normally distributed population, you can also determine what the probability is of certain data occurring .

For example, if the mean of a normally distributed data is 56 and the standard deviation is 10, you know that 68% of your data will fall between 46 and 66 (one standard deviation below and above the average).

3.Forecasting is possible because even without knowing all data specifics, projections can be made as to where data will fall within the set, based on the 68%, 95%, and 99.7% dictates showing where all data should rest.

orchestra answered 1 year ago

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