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# HELPPPPP

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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.

Dec 28, 2020

#1
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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)

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

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

$$\text{Median} = 9$$

$$\text{Mode} = 7$$

$$\text{Mean} = 7.975 = 8$$

Credit to CPhill; https://web2.0calc.com/questions/basic-stats_2#r1

P.S. I changed up CPhill's answer a little, so please give me a little credit also!

Dec 29, 2020
#2
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The answer is actually 7.9, but thnx!

Leafie  Dec 29, 2020
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Ah, sorry about that, you may give me a downvote for that. I'm sorry.

cryptoaops  Dec 29, 2020