Empirical Rule Calculator

The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule. The Empirical Rule Calculator helps you find the 68-95-99.7 Rule for the given set of data.

68-95-99.7 Rule Calculator

Total Numbers
Mean (Average)
Standard Deviation
Empirical Rule at 68% falls between
Empirical Rule at 95% falls between
Empirical Rule at 97.7% falls between

The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule. The Empirical Rule Calculator helps you find the 68-95-99.7 Rule for the given set of data.

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Empirical Rule :

1. At 68 % the rule is,
= (Mean - std) and (Mean + std)

2. At 95% the rule is,
= (Mean - 2 × std) and (Mean + 2 × std)

3. At 97.7% the rule is,
= (Mean - 3 × std) and (Mean + 3 × std)

Empirical rule is the statistical rule for a normal distribution determined with the mean and the standard deviation. It is the statistical rule stating that for a normal distribution, where most of the data will fall within three standard deviations of the mean. The empirical rule can be broken down into three parts: 68% of data falls within the first standard deviation from the mean. 95% fall within the 2nd standard deviations. 99.7% fall within third standard deviation. You can enter any set of numbers separated by comma in this Empirical Rule Calculator, and you could see the results such as mean, standard deviation, empirical rule at 68%, 95% and 97.7%. Hence the empirical rule is known as 68-95-99.7 rule.

Example:

Find the empirical rule for a set of data 12, 65, 23, 74

Step 1 :

Mean = Sum of X values / N (Number of values)
= (12+65+23+74) / 4
= 174 / 4
= 43.5

Step 2 :

The standard deviation is 30.6

Step 3 :

Using the mean and standard deviation,
68 % data falls between 12.9 and 74.1
95 % of the values fall between -17.7 and 104.7
97.7 % of the values fall between -48.3 and 135.3

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