Let's work through the questions step-by-step.
(i) Finding the mean to determine A's average number of points scored per game:
Player A played three games and scored the following points:
- Game 1: 15 points
- Game 2: 12 points
- Game 3: 8 points
To find the mean (average) score for A, sum the points and divide by the number of games played:
[tex]\[
\text{Total points scored by A} = 15 + 12 + 8 = 35
\][/tex]
[tex]\[
\text{Number of games A played} = 3
\][/tex]
[tex]\[
\text{Mean points scored by A per game} = \frac{35}{3} \approx 11.67
\][/tex]
So, A's average number of points scored per game is approximately 11.67 points.
(ii) To find the mean number of points per game for C, would you divide the total points by 3 or by 4? Why?
Player C played in all four games and scored the following points:
- Game 1: 10 points
- Game 2: 0 points
- Game 3: 19 points
- Game 4: 18 points
Since C played in all four games, we need to divide by 4 to find the mean. The total points scored by C is:
[tex]\[
\text{Total points scored by C} = 10 + 0 + 19 + 18 = 47
\][/tex]
[tex]\[
\text{Number of games C played} = 4
\][/tex]
[tex]\[
\text{Mean points scored by C per game} = \frac{47}{4} = 11.75
\][/tex]
Thus, we divide by 4 because C played in all four games. The mean number of points C scored per game is 11.75 points.
(iii) B played in all four games. How would you find the mean?
Player B's points for the four games are as follows:
- Game 1: 9 points
- Game 2: 16 points
- Game 3: 0 points
- Game 4: 15 points
To calculate the mean, sum the points and divide by the number of games:
[tex]\[
\text{Total points scored by B} = 9 + 16 + 0 + 15 = 40
\][/tex]
[tex]\[
\text{Number of games B played} = 4
\][/tex]
[tex]\[
\text{Mean points scored by B per game} = \frac{40}{4} = 10
\][/tex]
So, B's average number of points scored per game is 10 points.
Who is the best performer?
We compare the mean points scored per game by each player:
- A: 11.67 points per game
- B: 10 points per game
- C: 11.75 points per game
The highest mean points per game is 11.75, which belongs to Player C.
Therefore, the best performer is Player C.
