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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

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[OUTPUT]

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[ACTION NAME]

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system
In a baseball league, the number of home runs hit in May by the top players is shown in the graph below. Calculate the mean (average) number of home runs per game hit by these players, knowing that each player played an unequal number of games, as indicated.

[asy]
draw((18,0)--(0,0)--(0,18));
label("5",(3,-1)); // 5 players hit 4 home runs
label("6",(6,-1)); // 6 players hit 5 home runs
label("7",(9,-1)); // 4 players hit 7 home runs
label("8",(12,-1)); // 3 players hit 9 home runs
label("9",(15,-1)); // 2 players hit 11 home runs
fill((3,.5)..(3.5,1)..(3,1.5)..(2.5,1)..cycle); // 5 players
fill((3,2)..(3.5,2.5)..(3,3)..(2.5,2.5)..cycle);
fill((3,3.5)..(3.5,4)..(3,4.5)..(2.5,4)..cycle);
fill((3,5)..(3.5,5.5)..(3,6)..(2.5,5.5)..cycle);
fill((6,.5)..(6.5,1)..(6,1.5)..(5.5,1)..cycle); // 6 players
fill((6,2)..(6.5,2.5)..(6,3)..(5.5,2.5)..cycle);
fill((6,3.5)..(6.5,4)..(6,4.5)..(5.5,4)..cycle);
fill((6,5)..(6.5,5.5)..(6,6)..(5.5,5.5)..cycle);
fill((6,6.5)..(6.5,7)..(6,7.5)..(5.5,7)..cycle);
fill((9,.5)..(9.5,1)..(9,1.5)..(8.5,1)..cycle); // 4 players
fill((9,2)..(9.5,2.5)..(9,3)..(8.5,2.5)..cycle);
fill((9,3.5)..(9.5,4)..(9,4.5)..(8.5,4)..cycle);
fill((12,.5)..(12.5,1)..(12,1.5)..(11.5,1)..cycle); // 3 players
fill((12,2)..(12.5,2.5)..(12,3)..(11.5,2.5)..cycle);
fill((15,.5)..(15.5,1)..(15,1.5)..(14.5,1)..cycle); // 2 players
label("Games Played:",(12,18));
label("5", (3,16)); // Games played by players who hit 4 home runs
label("6", (6,16)); // Games played by players who hit 5 home runs
label("8", (9,16)); // Games played by players who hit 7 home runs
label("10", (12,16)); // Games played by players who hit 9 home runs
label("12", (15,16)); // Games played by players who hit 11 home runs
label("Number of Home Runs",(9,-3));
picture perpLabel;
label(perpLabel,"Number of Top Players");
add(rotate(90)*perpLabel,(-1,9));
[/asy]

Present the answer in LaTex format: \boxed{Your answer}
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