Standard Deviation Equation Normal Distribution. I m thinking it has something to do with the empirical rule so 68 3 lies within one standard deviation of the mean etc. But hang on.
F x μ σ 2 1 σ φ x μ σ displaystyle f x mid mu sigma 2 frac 1 sigma varphi left frac x mu sigma right. A normal distribution is a very important statistical data distribution pattern occurring in many natural phenomena. The standard normal distribution also called the z distribution is a special normal distribution where the mean is 0 and the standard deviation is 1.
It also makes life easier because we only need one table the standard normal distribution table rather than doing calculations individually for each value of mean and standard deviation.
Lower range 65 3 5 3 54 5. S d x 1 x m 2 x 2 x m 2. If a data distribution is approximately normal then about 68 percent of the data values are within one standard deviation of the mean mathematically μ σ where μ is the arithmetic mean about 95 percent are within two standard deviations μ 2σ and about 99 7 percent lie within three standard deviations μ 3σ. Here is the standard normal distribution with percentages for every half of a standard deviation and cumulative percentages.
