Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912



Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

  1. What information is provided by the sign ( + / ) of a z-score? What information is provided by the numerical value of the z-score?

To determine

Information provided by +/- sign of Z score and what information by its numerical value.



The sign of the z-score tells whether the location is above (+) or below (-) the mean, and the magnitude tells the distance from the mean in terms of the number of standard deviations.


Z Score is given by the transformation=(X-mean)/standard deviation.

So, a Z score of (+) means to the right of mean and sign of (−) means right of the mean. Since Z scores are standardized scores hence the numerical value depicts distance from mean in terms of standard deviation or spread of the distribution. So, a Z=+2.00 implies the data point is 2 standard deviation about the mean and so on.

Z-Scores can help us understand how typical a particular score is within bunch of scores. If data are normally distributed, approximately 95% of the data should have Z-score between -2 and +2. Z-scores that do not fall within this range may be less typical of the data in a bunch of scores.

Z-Scores can help us compare individual scores from different bunches of data. We can use Z-scores to standardize scores from different groups of data. Then we can compare raw scores from different bunches of data.


We have mentioned the information conveyed by sign and numerical value of Z scores.

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