Total Points from Average Points

Date: 03/12/2001 at 21:12:17
From: monique fisher
Subject: Finding average or mean

Mandela's basketball team played six games, with an average or mean of 
50 points. How many points did the team score?

Date: 03/13/2001 at 09:26:57
From: Doctor Patti
Subject: Re: Finding average or mean

Hello Monique,

Thank you for writing to Dr. Math.

Mandela's team played 6 games. Their average score was 50 points. The 
average score is found by finding the total sum of the game scores and 
then dividing the total by the number of games. 

      Average = ( Score total ) / 6

Let's look at two specific situations.

Situation 1:

    Game 1:  42 points
    Game 2:  10 points
    Game 3:  84 points
    Game 4:  51 points
    Game 5:  62 points
    Game 6:  51 points

In this case, the average score is 50 because

    Score total = 42 + 10 + 84 + 51 + 62 + 51 

                = 300

             and

    Average = 300 / 6

            = 50

Situation 2:

    Game 1: 53 points
    Game 2: 52 points
    Game 3: 49 points
    Game 4: 46 points
    Game 5: 42 points
    Game 6: 58 points

In this case the average score is also 50 because

    Score total = 53 + 52 + 49 + 46 + 42 + 58

                = 300

            and

    Average = 300 / 6

            = 50

Do you notice a pattern? Look at the score totals.

I was able to these examples because:

    - I knew the average was 50;
    - six games were played;
    - multiplication would give me the the score total;
    - all I needed was to find six numbers whose total came to the 
      score total from the previous step.

I hope this helps you out. The answer is in the problem, but I hope 
that you will see where the number comes from.  Please write back if 
you have any other questions.

- Doctor Patti, The Math Forum
  http://mathforum.org/dr.math/