# Empirical Rule Calculator

Empirical rule or 3 Sigma rule. The empirical rule implies that under the normal deviation we have fixed values of data. Therefore, it is also known as the 68 95 and 99.7 rules as well.

For example, in a normal curve where the data is equally distributed about the mean, we have fixed values for the standard deviation according to the rule. Moving a step forward or backward from the mean of the curve means + or - Sigma(σ) or standard deviation. It may be , 2σ, or .

key points to be noted.

Under this rule, from or standard deviation, we mean that up to 68% of data fall in the curve. Furthermore, for , we mean that 95% that is false under the curve. Lastly,  means that 99.7% falls in this region.

## Formula of Empirical Rule Calculator

However, there is no defined formula but you can have a simple equation in order to solve a complicated dataset. i.e.,

x ± standard deviation (either 1σ, 2σ or 3σ)

### Example

To make the process easier for you, we can have an illustration with the help of an example.

Suppose we have a history of previous school results, having a normal distribution with the mean of 82 but the standard deviation is 6.

Now we have to find the range around the mean including 95% of the grade.

x = 82

σ = 6


From the empirical formula, we find that the standard deviation for 95 falls in 2σ.

Applying the empirical rule in a simple way.

x + 2σ = 82 + 2(6)

82 + 12 = 94


Also,

x - 2σ = 82 - 2(6)
82 - 12 = 70

So this is the average number of scores the students can achieve under the mentioned standard deviation about the mean value.