Enter the mean and standard deviation into the calculator to determine the range. This calculator can also evaluate any of the variables given the others are known.
- Empirical Rule Calculator (68%, 95%, 99.7%)
- Standard Deviation of the Poisson Distribution Calculator
- Relative Standard Deviation Calculator
2 Standard Deviation Rule Formula
The following formula is used to calculate the 2 Standard Deviation Rule.
Range = μ ± 2σ
Variables:
- Range is the range within which about 95% of the data points fall
- μ is the mean of the data set
- σ is the standard deviation of the data set
To calculate the 2 Standard Deviation Rule, first find the mean (μ) and the standard deviation (σ) of the data set. Then, add and subtract two times the standard deviation from the mean. This will give you the range within which about 95% of the data points fall.
What is a 2 Standard Deviation Rule?
The 2 Standard Deviation Rule, also known as the Empirical Rule, is a statistical rule which states that for a normal distribution, almost all data will fall within three standard deviations of the mean. Specifically, about 68% of data falls within one standard deviation, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. This rule is used to determine the standard deviation of a data set and to predict where a particular data point might fall in relation to the mean.
How to Calculate 2 Standard Deviation Rule?
The following steps outline how to calculate the 2 Standard Deviation Rule.
- First, determine the mean of the data set (μ).
- Next, determine the standard deviation of the data set (σ).
- Next, use the formula Range = μ ± 2σ to calculate the range within which about 95% of the data points fall.
- Finally, calculate the 2 Standard Deviation Rule.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Range = ?
μ = ?
σ = ?
