## Statistics - Range Rule of Thumb - Tutorialspoint.

In a normal distribution, about 68% of a sample is within one standard deviation of the mean. About 95% is within two standard deviations. And about 99.7% is within three standard deviations. The numbers in the figure above mark standard deviations from the mean. The z value is the distance between a value and the mean in terms of standard deviations. In the figure above, each number is a z.

Standard Deviation. In probability and statistics, the standard deviation of a random variable is the average distance of a random variable from the mean value. It represents how the random variable is distributed near the mean value. Small standard deviation indicates that the random variable is distributed near the mean value.

Enter the mean and standard deviation for the distribution. Enter the chosen values of x 1 and, if required, x 2 then press Calculate to calculate the probability that a value chosen at random from the distribution is greater than or less than x 1 or x 2, or lies between x 1 and x 2.

The formula for the sample standard deviation (s) iswhere x i is each value is the data set, x-bar is the mean, and n is the number of values in the data set. To calculate s, do the following steps:. Calculate the average of the numbers, Subtract the mean from each number (x).

In probability theory and statistics, the geometric standard deviation (GSD) describes how spread out are a set of numbers whose preferred average is the geometric mean.For such data, it may be preferred to the more usual standard deviation.Note that unlike the usual arithmetic standard deviation, the geometric standard deviation is a multiplicative factor, and thus is dimensionless, rather.

A Z-Score is a statistical value that tells you how many standard deviations a particular value happens to be from the mean of the entire data set. You can use AVERAGE and STDEV.S or STDEV.P formulas to calculate the mean and standard deviation of your data and then use those results to determine the Z-Score of each value.

To introduce a method of estimating the mean and standard deviation based on the median, range and sample size. Therefore, the quantitative data without providing the mean and standard deviation.