Finding data

[ksierra]

Desrie played 6 basketball games. The mean was 18 points. The range was 8 points. What might each of her scores be?

I had 6 lines to represent numbers. The largest number I used was 18, the smallest 8 to represent my range. I am stuck after here. I think that all my numbers when added together should equal 108. What am I doing wrong?

 

[mmm4444bot]

… What am I doing wrong?

It seems to me that you've misunderstood the term "range".

The range of a set of numbers is simply the difference between the smallest and largest numbers in the set.

So, you're looking for six numbers whose average is 18, where the difference between the largest and smallest is 8.

You've got the total of the six numbers correct, since 108/6 = 18.

Hint: Her scores in some of the games could be the same; in other words, the six numbers do not all need to be different. (I'm thinking of solving a system of two equations.)

Cheers ~ Mark

 

[soroban]

Hello, ksierra!

Desrie played 6 basketball games. The mean was 18 points. The range was 8 points. What might each of her scores be?

\(\displaystyle \text{Here is a very primitive way to create a set of scores.}\)


\(\displaystyle \text{The mean (average) of the 6 scores is 18.}\)
\(\displaystyle \text{She might have scored 18 points in }every\text{ game: }\;\;\begin{array}{ccc} \quad& 18 & \quad \\ & 18 & \\ & 18 & \\ & 18 & \\& 18 & \\ & 18 & \\ \hline \end{array}\)


\(\displaystyle \text{But the range is 8 (the difference between the highest and lowest scores).}\)


\(\displaystyle \text{Move one of the 18s }down\text{ 4 points, move another }up\text{ 4 points: }\;\;\begin{array}{ccc} \quad & 18 & \quad\\ & 18 & \\ & 18 & \\ 14 & 18 & 22 \\ \hline \end{array}\)

. . \(\displaystyle \text{and this set of scores satisfies the requirements of the problem.}\)


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


\(\displaystyle \text{We can get even more creative:}\)

\(\displaystyle \text{Move one of the 18s down 2 points, move another up 2 points: }\;\;\begin{array}{ccccc}\quad & \quad & 18 & \quad & \quad \\ 14 & 16 & 18 & 20 & 22 \\ \hline \end{array}\)


Get the idea?