Question

# Jenny played four games of golf. For these games her modal score was 76 and her mean score was 75. Her range of scores was 10. What were her scores for the four games?

Answer

Jenny's scores for the four games are [70, 76, 76, 80].

- Find the sum of scores A.
- Use the equation Mode = (2*median - sum of scores)/2 to find the median M.
- Use the equation Mean = sum of scores/4 to find the mean X.
- Let Y and Z be Jenny's lowest and highest score. We have: 75=X => X=(A+Y+76+Z)/4; 76=(2*M-A)/2 => 2*M-A=152; and 10=Z-Y => Z=Y+10. Putting these three equations together we get {(A-304)=2*Y+2*M => A-152=Y+M; 304=4*X => A=4*X}; substituting the value Y+M=A/2-152/2 and A=4*X into the first equation, we have Y+M=2*X-76.
- Solving for Y+M and Y-M, we get Y+M=149 and Y-M=Z-M=5; hence Y=(Z-5)/2 and M=(Y+M)/2.