Final answer:
Marcus needs a score of 367 in his next game to have a mean of exactly 325. This was calculated by first determining the total points he has so far, and then figuring out what additional score will bring his mean to 325 after the next game.
Step-by-step explanation:
To find out the score Marcus needs in his next game to have a mean of exactly 325, we'll first calculate the total points he has scored so far and then determine what additional score will bring his mean to 325.
To calculate the total score from the given points, add up the individual round scores: 236 + 342 + 328 + 352 + 352 + 306 + 317.
This gives us a total score of 2233 points over 7 games.
Since the mean score is the total score divided by the number of games, we want the total score after 8 games to be 8 times the desired mean: 8 * 325 = 2600.
To find out the score needed in the next game, subtract the current total score from the desired total score after 8 games: 2600 - 2233 = 367.
Therefore, Marcus needs a score of 367 in his next game to have a mean of exactly 325.