The mean of a certain number of observations is 35. What is the new value of the mean if each observation is :
divided by 5.

Answer

To find the new mean when each observation is divided by 5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
We know that the mean of a certain number of observations is 35.

2. **Let the Number of Observations be n**:
We will denote the number of observations as \( n \).

3. **Calculate the Sum of Observations**:
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} \]
Given that the mean is 35, we can express the sum of observations as:
\[ \text{Sum of Observations} = \text{Mean} \times \text{Number of Observations} = 35 \times n = 35n \]

4. **Dividing Each Observation by 5**:
If each observation is divided by 5, we can factor out \( \frac{1}{5} \) from each observation. Thus, the new sum of observations becomes:
\[ \text{New Sum of Observations} = \frac{1}{5} \times \text{Sum of Observations} = \frac{1}{5} \times 35n = \frac{35n}{5} = 7n \]

5. **Calculate the New Mean**:
The new mean can be calculated by dividing the new sum of observations by the total number of observations:
\[ \text{New Mean} = \frac{\text{New Sum of Observations}}{\text{Number of Observations}} = \frac{7n}{n} = 7 \]

### Final Answer:
The new mean after dividing each observation by 5 is **7**.