# 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 **1σ**, **2σ,** or **3σ**.

**key points** to be noted.

Under this rule, from **1σ** or **standard deviation**, we mean that up to **68%** of data fall in the curve. Furthermore, for **2σ**, we mean that **95% **that is false under the curve. Lastly, **3σ** 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.

**Note:**Visit our Relative Standard Deviation Calculator to know more about the standard deviation.

### Calculator use

By using the empirical rule calculator, you can find the upper and lower limit deviation by simply putting the value of the mean and deviations. In other words, you have to give your graph a written form.

Afterward, you have to click on the button in order to get your upper and lower limits. In case you don't have the exact percentage of standard deviation. Simply place your percentage and the algorithm will automatically find the deviation.

It is a better way to solve complex statistical equations.