+0  
 
+2
120
3
avatar+82 

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
avatar+117 
+1

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)

 

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
avatar+82 
+1

The answer is actually 7.9, but thnx!

Leafie  Dec 29, 2020
 #3
avatar+117 
-2

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

cryptoaops  Dec 29, 2020

38 Online Users

avatar
avatar