   Chapter 5, Problem 1P Statistics for The Behavioral Scie...

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

Solutions

Chapter
Section Statistics for The Behavioral Scie...

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

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.

Solution:

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.

Explanation

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.

Conclusion:

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

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