The empirical rule calculator is designed to apply the 68-95-99.7 rule to a given dataset for a normal distribution. It determines the range of values within 1, 2, and 3 standard deviations from the mean.

- First, input the mean (average) and standard deviation of a dataset.
- Press the 'Calculate' button to obtain the results.
- Finally, the tool returns the range of values corresponding to 68%, 95%, and 99.7% of the data.

The Empirical Rule also called the 68-95-99.7 Rule, defines how data in a normal distribution is spread out from the mean. It states:

- 68% of the data falls within 1 standard deviation of the mean.
- 95% of the data falls within 2 standard deviations of the mean.
- 99.7% of the data falls within 3 standard deviations of the mean.

The formula to apply the Empirical Rule is:

68% of data falls between: μ − (1 × σ) and μ + (1 × σ).

95% of data falls between: μ − (2 × σ) and μ + (2 × σ).

99.7% of data falls between: μ − (3 × σ) and μ + (3 × σ).

Let's take an example.

Suppose, the mean is 23.5 and the standard deviation is 5. Find the range of data points between 68%, 95%, and 99.7% of the data.

1. 68% of data lies between:

23.5 - 5 = 18.5 and 23.5 + 5 = 28.5.

2. 95% of data lies between:

23.5 - (2 × 5) = 13.5 and 23.5 + (2 × 5) = 33.5.

3. 99.7% of data lies between:

23.5 - (3 × 5) = 8.5 and 23.5 + (3 × 5) = 38.5.

The ranges in an example represent how data is distributed in a normal distribution curve.