# A z score is a measure of relative standing for an

Last updated: 2/2/2024

A z score is a measure of relative standing for an observation because it tells us the number of standard deviations and direction an observation is from the mean In other words when we use the standard deviation as our measurement unit the absolute value of the z score tells us how far an observation is from the mean in number of standard deviations It is positive when the observation is found above to the right or greater than the mean and negative when the observation is found below to the left or less than the mean The following is the formula to compute the z score for an observation x from a population with mean and standard deviation d Alternatively when working with a sample instead of a population this formula is used with sample mean x and sample standard deviation s Recall the following summary statistics for our sample of white wine pH measurements Z Variable Name pH Wines with low pH taste tart and crisp whereas wines with higher pH are more susceptible to bacterial growth A pH of about 3 0 to 3 4 is most desirable for white wines z X X S 3 0 1 25 x 0 Z X X S X X 5 z score for pH of 3 4 3 4 1 25 Determine the relative standing for a pH of 3 0 and a pH of 3 4 by computing a z score for each observation using the rounded values above and rounding each z score to two decimals z score for pH of 3 0 3 1883 0 1510 3 1883 0 1510 N Mean X Standard Deviation 4 898 3 1883 0 1510 Median 3 18 Minimum Value 2 72 Taking the absolute value of each z score gives the following interpretations for each pH Maximum Value 3 82