If the mean of 15 observations is 16, find the sum of the 15 observations.

Answer

To find the sum of the 15 observations given that the mean is 16, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mean Formula**:
The mean (average) of a set of observations is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
In this case, we know the mean is 16 and the number of observations is 15.

2. **Set Up the Equation**:
Using the formula for mean, we can set up the equation:
\[ 16 = \frac{\text{Sum}}{15} \]

3. **Rearrange the Equation to Find the Sum**:
To find the sum, we can rearrange the equation:
\[ \text{Sum} = 16 \times 15 \]

4. **Calculate the Sum**:
Now, we perform the multiplication:
\[ 16 \times 15 = 240 \]

5. **Conclusion**:
Therefore, the sum of the 15 observations is:
\[ \text{Sum} = 240 \]

### Final Answer:
The sum of the 15 observations is **240**.

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