After `9` games, the mean number of goals scored by a football team is `3`.If after one more game

they score `5` goals, what is the new mean value of goals scored?

Options

A. `4`
B. `2.5`
C. `3`
D. `3.2`

Answer

To find the new mean value of goals scored by the football team after one more game, we can follow these steps:

### Step 1: Calculate the total goals scored in the first 9 games.
Given that the mean number of goals scored after 9 games is 3, we can use the formula for mean:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

Let \( x \) be the total number of goals scored in the first 9 games. Therefore, we have:

\[ 3 = \frac{x}{9} \]

### Step 2: Solve for \( x \).
To find \( x \), we can rearrange the equation:

\[ x = 3 \times 9 = 27 \]

So, the total goals scored in the first 9 games is 27.

### Step 3: Add the goals scored in the 10th game.
After one more game, the team scores 5 goals. Therefore, the new total goals scored is:

\[ \text{Total goals} = 27 + 5 = 32 \]

### Step 4: Calculate the new mean.
Now, the total number of games played is 10 (9 + 1). We can calculate the new mean using the total goals scored:

\[ \text{New Mean} = \frac{\text{Total goals}}{\text{Total games}} = \frac{32}{10} = 3.2 \]

### Conclusion:
The new mean value of goals scored by the football team after 10 games is **3.2**.

---