Standard Deviation Equation Normal Distribution. 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. The standard normal distribution follows the 68 95 99 70 rule which is also called as the empirical rule and as per that sixty eight percent of the given data or the values shall fall within 1 standard deviation of the average or the mean while ninety five percent shall fall within 2 standard deviations and finally the ninety nine decimal seven percent of the value or the data shall fall within 3 standard deviations of the average or of the mean.
From a set of data with n values where x 1 represents the first term and x n represent the nth term if x m represents the mean then the standard deviation can be found as follows. S d x 1 x m 2 x 2 x m 2. Sum 6 25 20 25 2 25 6 25 30 25 0 25 65 5.
Here is the standard normal distribution with percentages for every half of a standard deviation and cumulative percentages.
S d x 1 x m 2 x 2 x m 2. Any normal distribution can be standardized by converting its values into z scores. X n x m 2 n. Sum 6 25 20 25 2 25 6 25 30 25 0 25 65 5.
