Equation to approximate percent likelyhood of different sigma events

In summary, the normal distribution formula or the 68-95-99.7 rule is commonly used to approximate the percent likelihood of different sigma events. It is derived from the properties of the normal distribution and is widely used in statistics and probability. While it can be applied to approximately normal distributions or those with a large sample size, it is not suitable for non-normal distributions. The accuracy of the equation in predicting the likelihood of events depends on factors such as sample size and the shape of the distribution. One limitation is that it assumes a symmetrical distribution around the mean and does not account for outliers or extreme values. It is important to use the equation with caution and consider its limitations when interpreting the results.
  • #1
jaydnul
558
15
Hi!

I was wondering if there was an equation to plug in a standard deviation value and get back approximately the percent likely hood of getting that sigma (for example 1 sigma would be 33%, 3 sigma 0.27%, etc).

Just something that approximates it with algebra, no calculus

Thanks!
 
Mathematics news on Phys.org

1. What is the equation used to approximate the percent likelihood of different sigma events?

The equation used to approximate the percent likelihood of different sigma events is known as the Standard Deviation Rule or the 68-95-99.7 rule. It states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

2. How is the equation derived?

The equation is derived from the normal distribution curve, also known as the bell curve, which represents the probability distribution of a continuous random variable. The curve is symmetric and follows the 68-95-99.7 rule, with the mean at the center and standard deviations on either side.

3. Can the equation be used for any type of data?

The equation can be used for any type of data that follows a normal distribution, which is a common assumption in many statistical analyses. However, if the data does not follow a normal distribution, the equation may not accurately approximate the percent likelihood of different sigma events.

4. How accurate is the equation?

The equation is a good approximation for data that follows a normal distribution, but it is not exact. In reality, the percentage of data falling within each standard deviation may vary slightly from the 68-95-99.7 rule. However, for large sample sizes, the equation becomes more accurate.

5. How is the equation useful in scientific research?

The equation is useful in scientific research as it provides an estimate of the likelihood of different sigma events, which can help researchers make decisions and draw conclusions. It also allows for comparisons between different data sets and helps identify outliers or unusual data points.

Similar threads

B Sigma Multiplied Gaussian Distribution
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
I Optimization problem with multiple outputs: impossible?
    • General Math
Replies
6
Views
1K
B Calculating Percents: A/B vs. B/A
    • General Math
Replies
7
Views
1K
I Cubic Algebraic Solution: Understanding the Approximation in Equations 4 and 5
    • Calculus
Replies
5
Views
1K
I Some notes on stochastic physics
    • Classical Physics
Replies
0
Views
148
A Derivation of free fields... coefficient question
    • High Energy, Nuclear, Particle Physics
Replies
5
Views
985
A The μ in dimensional regularization
    • High Energy, Nuclear, Particle Physics
Replies
4
Views
1K
I On error estimates of approximate solutions
    • Differential Equations
Replies
1
Views
669
MHB Least squares method : approximation of a cubic polynomial
    • General Math
Replies
3
Views
2K
I Dirac equation in the hydrogen atom
    • Quantum Physics
Replies
1
Views
902

Hot Threads

Recent Insights

Back
Top