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Laura will have seven test scores at the end of the semester. Each of the scores is a positive integer less than or equal to 100. Her first five scores are 80,83,87,94, and 96. How many different values are possible for the median of her seven scores?

 Sep 29, 2020
 #1
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There are 5 different possible values for the median.

 Sep 29, 2020
 #2
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its 12

 Sep 29, 2020
 #3
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Is it 12 ?   Hmmmm.....

 

80 83    87     94 96     currently 87 is the median   

                                    if the next two scores are >87

80  83 87 x x  94 96     one of the x's becomes the median  (x could be 87 -100)    (14 ways)

                                    if one is higher than 87 and one is lower

 

80 83 x 87 x 94 96      87 is the median  (1)

                                    if both are lower than 87

 

80 83 x x 87 94 96    one of the x's becomes the median  x could be any score 1 - 86  (86 ways)  ('0' score not possible)

 

So I THINK it is 14 + 1 + 86 different median scores

 Sep 29, 2020
edited by ElectricPavlov  Sep 29, 2020

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