Finding data

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?

Hello, ksierra!

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

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


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


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


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

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


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


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

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


Get the idea?