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.

helpppp Apr 4, 2020

#1**+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

CPhill Apr 4, 2020