To calculate the mean number of goals per game in a soccer league, we can follow these steps:
1. Understand the Data:
We have two arrays:
- Goals: [tex]\([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\)[/tex]
- Frequency: [tex]\([17, 15, 12, 11, 11, 13, 21, 9, 10, 9]\)[/tex]
2. Calculate the Total Number of Games:
The total number of games is the sum of the frequencies of all the goals.
[tex]\[
\text{Total games} = 17 + 15 + 12 + 11 + 11 + 13 + 21 + 9 + 10 + 9 = 128
\][/tex]
3. Calculate the Total Number of Goals Scored:
To find the total number of goals scored, we multiply each goal value by its corresponding frequency and sum the results.
[tex]\[
\text{Total goals} = (0 \times 17) + (1 \times 15) + (2 \times 12) + (3 \times 11) + (4 \times 11) + (5 \times 13) + (6 \times 21) + (7 \times 9) + (8 \times 10) + (9 \times 9)
\][/tex]
[tex]\[
= 0 + 15 + 24 + 33 + 44 + 65 + 126 + 63 + 80 + 81 = 531
\][/tex]
4. Calculate the Mean Number of Goals per Game:
The mean number of goals per game is obtained by dividing the total number of goals by the total number of games.
[tex]\[
\text{Mean goals per game} = \frac{\text{Total goals}}{\text{Total games}} = \frac{531}{128} \approx 4.1484375
\][/tex]
Thus, the mean number of goals per game is approximately [tex]\(4.1484375\)[/tex].
Considering the options provided:
A. 4.1 \
B. 4.0 \
C. 4.2 \
D. 3.8
The closest value to our calculated mean is 4.1.
Therefore, the correct answer is:
[tex]\[
\boxed{4.1}
\][/tex]
