how the z score is used
in it s most basic form the z score allows you determine how far measured in standard deviations the returns for the stock you re evaluating are from the mean of a sample of stocks the average score you have could be the mean of a stock s annual return the average return of the index it is listed on or the average return of a selection of stocks you ve picked some traders use the z scores in more advanced evalulation methods such as weighting each stock s return to use factor investing where stocks are evaluated based on specific attributes using z scores and standard deviation in the forex markets traders use z scores and confidence limits to test the capability of a trading system to generate winning and losing streaks z scores vs standard deviationin most large data sets assuming a normal distribution of data 99 7 of values lie between 3 and 3 standard deviations 95 between 2 and 2 standard deviations and 68 between 1 and 1 standard deviations standard deviation indicates the amount of variability or dispersion within a given data set for instance if a sample of normally distributed data had a standard deviation of 3 1 and another had one of 6 3 the model with a standard deviation sd of 6 3 is more dispersed and would graph with a lower peak than the sample with an sd of 3 1 a distribution curve has negative and positive sides so there are positive and negative standard deviations and z scores however this has no relevance to the value itself other than indicating which side of the mean it is on a negative value means it is on the left of the mean and a positive value indicates it is on the right the z score shows the number of standard deviations a given data point lies from the mean so standard deviation must be calculated first because the z score uses it to communicate a data point s variability 