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On her daily homework assignments, Qinna has earned the maximum score of $10$ on $15$ out of $40$ days. The mode of her $40$ scores is $7$ and her median score is $9$. What is the least that her arithmetic mean could be? Express your answer as a decimal to the nearest tenth.

 Apr 4, 2020
 #1
avatar+111329 
+2

Not sure  about this....but  here's  my rational

 

We  know that  we  have  15  scores of 10

 

Since  the  mode is  7  we  need to have  16  scores of 7  (and no more than this )

 

The  median  is  9, so the 20 and 21st  scores  must be  9....to keep the average as small as possible

 

And the other  3  scores  need to be  as small as possible so let them  =1

 

We  have

 

1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 ,7, 7, 9 ,9, 9, 9, 9, 9,10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

 

Median  = 9

Mode = 7

Mean   = 7.975  =  8

 

cool cool cool

 Apr 4, 2020

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