Empirical Rule Calculator

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