Empirical Rule Calculator

Empirical rule is the statistical rule for a normal distribution determined with the mean and the standard deviation. According to it, 68 % of data falls within first SD, 95 % within first two SD and 99.7 % within first three SD's. Hence it is also known as 68-95-99.7 or three sigma rule. Find the Empirical rule for the given set of data using this calculator.

68-95-99.7 Rule Calculation

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
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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)

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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