Is mean always one of the observations in a given data?

Answer

To determine whether the mean is always one of the observations in a given data set, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mean**: The mean (or average) of a set of numbers is calculated by adding all the numbers together and then dividing by the total number of observations.

2. **Choose a Data Set**: Let's consider a simple data set: 8, 4, and 3.

3. **Calculate the Mean**:
- First, add the numbers together:
\[ 8 + 4 + 3 = 15 \]
- Next, divide the total by the number of observations (which is 3 in this case):
\[ \text{Mean} = \frac{15}{3} = 5 \]

4. **Compare the Mean with the Observations**: Now, we check if the calculated mean (5) is one of the original numbers in the data set (8, 4, 3).

5. **Conclusion**: Since 5 is not one of the observations (8, 4, or 3), we can conclude that the mean is not always one of the observations in a given data set.

### Final Statement:
Therefore, the mean is not always one of the observations in a given data set.

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