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    Hello,

    While reading through a past paper I came to this question, which I became stuck on. I had a go at it and was wondering if you could check to see if it is right:

    Last Monday, a class of studnets took a test, and the highest percentage score was 92%. When the tests were returned, the highest scoring student discovered an adding up error in her test. After correcting this, her score was 95%. Indicate whether changing the students score made each of the summary statistics increase, decrease or stay the same.

    Provide Explanations

    a) Mean
    b) Median
    c) Range
    d) IQR
    e) Standard Deviation


    Here is my answer:

    Mean The mean mark will increase because to work out the mean you have to add up everyones score and divide by number of students and as the mark has changed, then mean will.

    Median The median mark will stay the same because the mark only effected the highest score student and not everyones mark was wrong.

    Range The range will increase as the top score has changed meaning the difference between the top score and the bottom score is bigger.

    IQR The IQR will remain the same as there is no effect on the upper and lower quartiles.

    Standard Deviation The standard deviation will increase as the mean has done.

    Thank you
    xx
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    Seems good to me.

    The standard deviation will increase because the deviation of an extreme value has increased, and by more than the concomittant increase in the mean.
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    (Original post by stem01)
    Mean The mean mark will increase because to work out the mean you have to add up everyones score and divide by number of students and as the mark has changed, then mean will.
    Fine, yeah. You might want to write it a bit more clearly, though, and state that as one mark has increased and the rest have stayed the same, their sum has increased, and so their mean has increased.

    (Original post by stem01)
    Median The median mark will stay the same because the mark only effected the highest score student and not everyones mark was wrong.

    Range The range will increase as the top score has changed meaning the difference between the top score and the bottom score is bigger.
    Both fine. Again, you might want to be clearer on the median that the highest score doesn't affect the score of the person right in the middle.

    (Original post by stem01)
    IQR The IQR will remain the same as there is no effect on the upper and lower quartiles.
    Yep, but why?

    (Original post by stem01)
    Standard Deviation The standard deviation will increase as the mean has done.
    Why? (What's your definition of standard deviation?)
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    Thanks for the replies. I thought that as the mean was in standard dviation and it increased, that it would as well.
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    (Original post by stem01)
    Thanks for the replies. I thought that as the mean was in standard dviation and it increased, that it would as well.
    sd measures how sprend out it around the mean. If the highest score increases then sd will increase because it is more sprend out around the mean.

    Well, say something like that.
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    (Original post by stem01)
    Thanks for the replies. I thought that as the mean was in standard dviation and it increased, that it would as well.
    Well, yes. But how do you know there aren't other factors involved? (As it happens, there are.)
 
 
 
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