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
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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.
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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Hi All,
We're told that a researcher computed the mean, median and the standard deviation for a set of performance scores, then 5 was added to each score. We're asked which of the 3 statistics would change. With a little logic - and the answer choices - we can answer this question without actually doing any math.
To start, whatever the current average of the scores is, if we add 5 to each score, then the average score WILL increase by 5. Thus, the mean does increase. Eliminate Answers B and C.
By increasing each score by 5, the median will also increase - since all of the numbers are each '5 bigger.' Thus, we need an answer that includes BOTH the mean and the median. Only one answer 'fits'...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're told that a researcher computed the mean, median and the standard deviation for a set of performance scores, then 5 was added to each score. We're asked which of the 3 statistics would change. With a little logic - and the answer choices - we can answer this question without actually doing any math.
To start, whatever the current average of the scores is, if we add 5 to each score, then the average score WILL increase by 5. Thus, the mean does increase. Eliminate Answers B and C.
By increasing each score by 5, the median will also increase - since all of the numbers are each '5 bigger.' Thus, we need an answer that includes BOTH the mean and the median. Only one answer 'fits'...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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When a constant number is added to all the elements of a data set, the mean and median increase by the same amount as the added constant, but the standard deviation does not change. Thus, the statistics that change are the mean and median.jamesk486 wrote:A researcher computed the mean, median and the standard deviation for a set of performance scores. If 5 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
If we did not know this fact, we could still find the answer by coming up with an example easy enough to calculate all three quantities. For instance, let's take a set where all the scores are equal, such as three scores of 10. In the original set, both mean and median are equal to 10; but the standard deviation is 0 (since standard deviation is a measure of how far away the elements are from the mean). When we add 5 to each element, we get three scores of 15; thus, the mean and median both increase to 15, but the standard deviation is still 0.
Answer: D
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