The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5 then the average of the whole group is

Options

A. `(15)/(4)`
B. `(1)/(5)`
C. 8
D. 4

Explanation

To find the average of the whole group based on the given data, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of observations and their averages:**
- Total number of observations = 40
- Average of the first 10 observations = 4.5
- Average of the remaining 30 observations = 3.5

2. **Calculate the total sum of the first 10 observations:**
\[ \text{Total sum of first 10 observations} = \text{Average} \times \text{Number of observations} = 4.5 \times 10 = 45 \]

3. **Calculate the total sum of the remaining 30 observations:**
\[ \text{Total sum of remaining 30 observations} = \text{Average} \times \text{Number of observations} = 3.5 \times 30 = 105 \]

4. **Calculate the total sum of all 40 observations:**
\[ \text{Total sum of all observations} = \text{Total sum of first 10} + \text{Total sum of remaining 30} = 45 + 105 = 150 \]

5. **Calculate the average of the whole group:**
\[ \text{Average of the whole group} = \frac{\text{Total sum of all observations}}{\text{Total number of observations}} = \frac{150}{40} = 3.75 \]

### Final Answer:
The average of the whole group is **3.75**.