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 of observations, we can follow these steps:

### Step 1: Identify the given data
- Total number of observations (n) = 40
- Number of observations in the first group (n1) = 10
- Average of the first group (x̄1) = 4.5
- Number of observations in the second group (n2) = 30
- Average of the second group (x̄2) = 3.5

### Step 2: Calculate the sum of observations for each group
- For the first group:
\[ \text{Sum of first group} = n1 \times x̄1 = 10 \times 4.5 = 45 \]

- For the second group:
\[ \text{Sum of second group} = n2 \times x̄2 = 30 \times 3.5 = 105 \]

### Step 3: Calculate the total sum of observations
- Total sum of observations:
\[ \text{Total sum} = \text{Sum of first group} + \text{Sum of second group} = 45 + 105 = 150 \]

### Step 4: Calculate the average of the whole group
- Average of the whole group:
\[ \text{Average} = \frac{\text{Total sum}}{n} = \frac{150}{40} = \frac{15}{4} = 3.75 \]

### Conclusion
The average of the whole group is \( \frac{15}{4} \) or 3.75.

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