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# Empirical Rule Calculator

Write the value of Mean and Standard Deviation and hit on calculate button to check the distribution of data by using this empirical rule calculator.

Table of Contents:

## Empirical Rule Calculator

Empirical Rule Calculator is a tool that takes mean & standard deviation as input and calculates the percentage of data points that fall within one, two, or three standard deviations from the mean, based on the Empirical Rule.

## What does "empirical rule" mean?

A statistical principle known as the** Empirical Rule **sometimes referred to as the **68-95-99.7 rule** or the **three-sigma rule**, offers a rough estimation of the distribution of data in a normal or bell-shaped distribution.

The purpose of making this rule is the idea that, in a normal distribution. The Empirical Rule asserts that if **X **is a random variable with a normal distribution and a mean and standard deviation, then **P (- X +) 0.68** (`about 68% of the data`

) and **P (- 2 X +) 0.95** (`roughly 95% of the data`

).

**P (- 3 X + 3) 0.997**around**99%**almost all.

Remember that the Empirical Rule functions most effectively with data that roughly resembles a normal distribution. The rule might not be as reliable if the data considerably deviates from a normal distribution.

In certain situations, more complex statistical techniques could be needed to adequately assess the data.

**Example**

Determine the data distribution when the mean (**μ**) = **32**, standard dev (**σ**) = **12**

**Solution**

**Step 1:**

First of all, we have to calculate the data falls between **68%**:

`= μ - σ, μ + σ`

**Step 2:**

Putting Values in Formula:

= 32 - 12

= 20

= 32 + 12

`= 44`

**Step 3:**

Now we have to **calculate **the data falls between **95%**:

`μ - 2σ, μ + 2σ`

Putting Values in Formula:

= 32 - 2(12)

= 32 - 24

**= 8**

= 32 + 2(12)

= 32 + 24

**= 56**

**Step 4:**

And then we have to calculate the data falls between **99.7%**:

`μ - 3σ, μ + 3σ`

Putting Values in Formula:

= 32 - 3(12)

= 32 - 36

**= -4**

= 32 + 3(12)

= 32 + 36

**= 68**

Hence the result is given below with the percentage of data distribution.

**68% of data falls between**

`20 and 44`

**95% of data falls between**

`8 and 56`

**99.7% of data fall between**

`-4 and 68`