If sum of x observations is 216 and their mean is 27. Then the number of observations is:

Options

A. 7
B. 8
C. 9
D. 10

Answer

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

### Step-by-step Solution:

1. **Understand the Formula for Mean**:
The mean (average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} \]
Let’s denote the number of observations as \( n \).

2. **Set Up the Equation**:
According to the problem, the sum of \( n \) observations is 216, and the mean is 27. We can set up the equation:
\[ 27 = \frac{216}{n} \]

3. **Rearrange the Equation**:
To find \( n \), we can rearrange the equation:
\[ n = \frac{216}{27} \]

4. **Calculate \( n \)**:
Now, we perform the division:
\[ n = \frac{216}{27} = 8 \]

5. **Conclusion**:
Therefore, the number of observations is \( n = 8 \).

### Final Answer:
The number of observations is **8**.