Average of 10 observation in a series is 64. If average of first 5 observation is 45 and last 3 observation is 71. Find the average of remaining.

Options

A. a. 91
B. b. 103
C. 3,1
D. None of the above

Answer

To solve the problem step by step, we need to find the average of the remaining observations after knowing the averages of the first five and the last three observations.

### Step-by-Step Solution:

1. **Calculate the Total of All Observations:**
- Given that the average of 10 observations is 64, we can find the total sum of these observations.
\[ \text{Total Sum} = \text{Average} \times \text{Number of Observations} = 64 \times 10 = 640 \]

2. **Calculate the Total of the First 5 Observations:**
- The average of the first 5 observations is given as 45.
\[ \text{Total of First 5 Observations} = 45 \times 5 = 225 \]

3. **Calculate the Total of the Last 3 Observations:**
- The average of the last 3 observations is given as 71.
\[ \text{Total of Last 3 Observations} = 71 \times 3 = 213 \]

4. **Calculate the Total of the Remaining Observations:**
- We now need to find the total of the remaining observations. There are 10 observations in total, and we have accounted for 5 (first) + 3 (last) = 8 observations.
- Therefore, the number of remaining observations is \(10 - 8 = 2\).
- The total of the remaining observations can be found by subtracting the totals of the first 5 and last 3 observations from the total sum of all observations.
\[ \text{Total of Remaining Observations} = \text{Total Sum} - (\text{Total of First 5} + \text{Total of Last 3}) \]
\[ = 640 - (225 + 213) = 640 - 438 = 202 \]

5. **Calculate the Average of the Remaining Observations:**
- Now, we can find the average of the remaining 2 observations.
\[ \text{Average of Remaining Observations} = \frac{\text{Total of Remaining Observations}}{\text{Number of Remaining Observations}} = \frac{202}{2} = 101 \]

### Final Answer:
The average of the remaining observations is **101**.