I have learned that z-scores are "Measures of Relative Standing" and that they can be used to compar

Yesenia Sherman

Yesenia Sherman

Answered question

2022-06-25

I have learned that z-scores are "Measures of Relative Standing" and that they can be used to compare two scores that are from different normal distributions.

For example if I wanted to compare how I performed

with a 85% in a math class with mean 70 and std dev 15;
and
with a 70% in a english class with mean 50 and std dev 15;

I would use the z-score formula to calculate a relative value for two situation and use it to compare them.

However why is it not enough just to compare each classes with the mean and use this as a basis for comparison? For example

85% -70% = 15%
70% - 50% = 20%
20 > 15 therefore I must have performed better in english

I know this is incorrect but I don't understand why. thx for the help

Answer & Explanation

Braylon Perez

Braylon Perez

Beginner2022-06-26Added 34 answers

This works fine when they have the same standard deviation (they are both 15 in this particular problem), but in general.
If the standard deviation were 5 for the math class, you'd have performed 3 standard deviations from the mean, which would be better than your Z-score for English.

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