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**babyangel1972****Member**- Registered: 2005-12-12
- Posts: 18

Let's say a student scored 45 on a math achievement test for which the mean was 36 and the standard deviation was 6. Judging on the basis of this performance, what score would you predict for her on a standardized test for which the mean is 100 and the standard deviation 15?

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

45-36=9 he is 9 points above mean.

9/6=1.5 he is 1.5 times of stdev above mean.

And this should always holds, regardless of the value of mean or stdev.

Why?

Suppose you can add all scores with 2 points, his will remain 9 points ahead.

Suppose you can multiply all scores by 2, his will be 18 points above mean, still 1.5 times of stdev.

Suppose he does as well as in the former test, he will still get a score 1.5 times of stdev above mean. This time, mean=100, stdev=15, he will get 122 or 123.

**X'(y-Xβ)=0**

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**babyangel1972****Member**- Registered: 2005-12-12
- Posts: 18

Thank You!

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

You are welcome

**X'(y-Xβ)=0**

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**brodr7630****Member**- Registered: 2013-01-27
- Posts: 1

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,013

Look at post #2.

Bob

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