Out Of This World Can You Use Standard Deviation For A Non Normal Distribution

It is somewhat ugly but you can see it depends upon the central location μ and the width σ.

Can you use standard deviation for a non normal distribution. The standard deviation alone is meaningful and it is essential to present it in descriptive. Like reliability analysis you can use a non-normal distribution to calculate process capability or alter-natively you can try to transform your data to follow a normal distribution using either the Box-Cox or Johnson transformation. Although we are not given particular values for the mean and standard deviation of the data we can still rely on the standardized normal distribution to make a general statement about all normal distributions.

Its shape can range from a normal curve to a decidedly non-normal curve. What is special about the standard deviation for the normal distribution is that it can be applied symmetrically about the mean since the normal is a symmetric distribution. Common Statistical Mistakes in Descriptive Statistics Reports of Normal and Non-Normal Variables in Biomedical Sciences Research.

About 68 of values drawn from a normal distribution are within one standard deviation σ away from the mean. Around 95 of values are within 2 standard deviations from the mean. I am pretty sure that the grade distribution is not normal but I do not know what it actually looks like.

More precisely the probability that a normal deviate lies in the range between and is given by. When you transform your data you modify the original data using a function of a variable. If the population standard deviation is known use the z-distribution.

It is also used as a simple test for outliers if the population is assumed normal and as a normality test if the population is potentially not normal. It so happens that the t-distribution tends to look quite normal as the degrees of freedom n-1 becomes larger than 30 or so so some users use this as a shortcut. What you mentioned about normal distribution is not really a condition for using z-score but an additional perk to z-score interpretation.

Formula of the normal distribution Optional You will not be working with the formula of the normal distribution explicitly too much in this course but if you are curious it is. Though other distributions such as the F T Chi-square Gamma or Beta are not consistently symmetric a variance - and therefore a standard deviation - can still be calculated for them. Mean and the standard deviation of the sample.