Question

I need help with the problem, "you have taken 5 quizzes and have a mean of 6 points. When you take a 6th quiz your mean is now 8 points. What is the score on the 6th quiz"?

Answer 1

how do we calculate a mean?

Answer 2

Add up the numbers and divide by the total numbers

Answer 3

then lets call x the sum of numbers for 5 quizzes

x/5 = 6

if we let y be the score of the last quiz, then (x+y)/6 = 8

solve for y

Answer 4

I don't get it

Answer 5

You don't get how amistre64 did that, or how to solve for \(y\), or what?

Answer 6

Let's take a simple example: you have two tests, and you got 6 and 8 points on them respectively. To calculate the mean, we add the scores and divide by the number of tests:
\[\text{average score} = \frac{6+8}{2} = \frac{14}{2} = 7\]

If we add another test, perhaps we got 10 points on this one, the calculation becomes
\[\text{average score} = \frac{6+8+10}{3} = \frac{24}{3} = 8\]

Notice that this is the same as taking the sum of the scores of the previous tests, adding the new test, and dividing by the new number of tests:
\[\frac{14+10}{3} = 8\]

Answer 7

Now, you say "but we don't know the total of the previous quizzes, how does this help?" But we do! We know that we had a mean of 6, and 5 quizzes, so for that to be true, we must have had \[\text{average score} = 6 = \frac{quiz1+quiz2+quiz3+quiz4+quiz5}{5}\]\[6 = \frac{\text{sum of quizzes}}{5}\]Multiply both sides by 5 and we find that the sum of the previous quizzes (called \(x\) by my distinguished colleague above) is\[\text{sum of quizzes} = 5*6= 30\]

Answer 8

So now we can work out the answer:

\[\text{average score after latest quiz} = 8 = \frac{\text{sum of previous quizzes} + \text{quiz 6 score}}{6}\]

You know the sum of the previous quizzes from my previous post, so you just need to do a bit of simple arithmetic to find the score for quiz 6.

Answer 9

The poster is off line, it was a monolog. I enjoyed it however, and it was a good step by step solution.

Answer 10

Yeah, I'm used to that happening, can only hope that they come back and get something from it!

Answer 11

They will get something from it, can't help but solve it.

Answer 12

If they come back, I guess they will have to close it. Actually amistre64 gave him the set up, he should of solved for x in the first equation, then substituted the value for x in the second equation and solved for y. But he "I don't get it" which is code for, "just gimme the answer"

Answer 13

But I digress lol.

Answer 14

I frequently take "I don't get it" as a challenge, and give them the benefit of the doubt until it becomes impossible to do otherwise. Often they are being lazy, but the reward when someone who honestly doesn't see it has the "aha!" moment makes up for a lot...

Answer 15

True, I hope I midjudged.

Answer 16

*misjudged

Answer 17

I would say that one "aha" is worth several "frustrations"