The mean of a data is 15 and the sum of the observations is 195. The number of observations is

Options

A. 13
B. 19
C. 16
D. 17

Answer

To find the number of observations given the mean and the sum of the observations, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Mean of the data (M) = 15
- Sum of the observations (S) = 195

2. **Use the Formula for Mean:**
The formula for mean is:
\[ \text{Mean} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} \]
This can be rearranged to find the number of observations (N):
\[ N = \frac{\text{Sum of Observations}}{\text{Mean}} \]

3. **Substitute the Given Values:**
Now, substitute the values of the sum of observations and the mean into the rearranged formula:
\[ N = \frac{195}{15} \]

4. **Perform the Division:**
Calculate the division:
\[ N = 13 \]

5. **Conclusion:**
The number of observations is 13.

### Final Answer:
The number of observations is **13**.