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OG 12 Diagnostic Test #9

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jamesk486 Master | Next Rank: 500 Posts Default Avatar
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OG 12 Diagnostic Test #9

Post Sat Jun 27, 2009 4:16 pm
A researcher computed the mean, median and the standard deviation for a set of performance scores. If were to be added to each score, which of the 3 statistics would change?

A. Mean only
B. Median only
C. SD only
D. Mean and median
E. The mean and SD only

I get really confused with these concepts often . Can someone explain pls the reasoning behind the answer? Thanks!

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Morgoth Master | Next Rank: 500 Posts
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Post Sat Jun 27, 2009 11:44 pm
Standard deviation

This means how evenly the numbers are spaced. Therefore, if the same number is added to the list the SD does not change. Also, another thing to remember is that SD is directly proportional to range of the list or set. SD will always be less than the range but if range changes, then SD will also change.

For example:

SET = 1,2,3,4

range = 4-1 = 3

if 5 is added to each number of the list

1+5, 2+5, 3+5, 4+5

6,7,8,9

range = 9-6 = 3

The range remains the same, therefore the SD will also be the same.

If you know this concept you can easily eliminate options C and E.

Median and Mean

1,2,3,4,5

In a consecutive number set, mean=median

Mean= Median = 3

if 5 is added to each number of the set

1+5,2+5,3+5,4+5,5+5

6,7,8,9,10

Mean = Median = 8

Mean and Median both change.

Lets see if the same happens in non-consecutive number set

2, 3, 5, 10

Mean = 20/4 = 5

Median = (3+5)/2 = 4

Now, add 5 to each of the numbers

7, 8, 10, 15

Mean = 40/4 = 10

Median = (8+10)/2 = 9

Mean and Median both change.

I dont know if your question is complete, but if you follow this method, I guess the answer should be D.

Hope this helps.

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