The runs scored by a batsman in `2` different cricket matches are as follows:
`65,32,97,0,32,160,68,23,35,75,40`
Which central tendency value will the batsman project for selection in the cricket team for a tournament?

Answer

To determine which central tendency value the batsman will project for selection in the cricket team for a tournament, we will calculate the mean of the runs scored by the batsman in the given matches.

### Step-by-Step Solution:

1. **List the Runs Scored**:
The runs scored by the batsman in the matches are:
\[ 65, 32, 97, 0, 32, 160, 68, 23, 35, 75, 40 \]

2. **Count the Number of Observations**:
Count the total number of matches (observations):
\[ \text{Number of observations} = 11 \]

3. **Calculate the Sum of Runs**:
Add all the runs together:
\[ 65 + 32 + 97 + 0 + 32 + 160 + 68 + 23 + 35 + 75 + 40 \]
Let's break it down:
- \( 65 + 32 = 97 \)
- \( 97 + 97 = 194 \)
- \( 194 + 0 = 194 \)
- \( 194 + 32 = 226 \)
- \( 226 + 160 = 386 \)
- \( 386 + 68 = 454 \)
- \( 454 + 23 = 477 \)
- \( 477 + 35 = 512 \)
- \( 512 + 75 = 587 \)
- \( 587 + 40 = 627 \)

Thus, the sum of runs is:
\[ \text{Sum} = 627 \]

4. **Calculate the Mean**:
The mean is calculated by dividing the sum of runs by the number of observations:
\[ \text{Mean} = \frac{\text{Sum}}{\text{Number of observations}} = \frac{627}{11} \]
Performing the division:
- \( 11 \) goes into \( 62 \) five times (since \( 11 \times 5 = 55 \)), leaving a remainder of \( 7 \).
- Bring down the \( 7 \) to make \( 77 \).
- \( 11 \) goes into \( 77 \) seven times (since \( 11 \times 7 = 77 \)), leaving a remainder of \( 0 \).

Therefore, the mean is:
\[ \text{Mean} = 57 \]

5. **Conclusion**:
The central tendency value that the batsman will project for selection in the cricket team is the mean, which is:
\[ \text{Mean} = 57 \]