The average of eight numbers is 14. The average of six of these numbers is 16. The average of the remaining two numbers is:Options :4816Data Inadequate

1. Break Down the Problem

We need to find the average of the remaining two numbers from a group of eight, given the overall average of the eight numbers and the average of six of these numbers.

2. Relevant Concepts

• The formula for the average:
  $\text{Average} = \frac{\text{Sum of elements}}{\text{Number of elements}}$

3. Analysis and Detail

1. Calculate the total sum of all eight numbers:
   Since the average of the eight numbers is 14:
   $\text{Total sum of eight numbers} = 14 \times 8 = 112$

2. Calculate the total sum of the first six numbers:
   Since the average of six of these numbers is 16:
   $\text{Total sum of six numbers} = 16 \times 6 = 96$

3. Calculate the sum of the remaining two numbers:
   $\text{Sum of two numbers} = \text{Total sum of eight numbers} - \text{Total sum of six numbers} = 112 - 96 = 16$

4. Calculate the average of the remaining two numbers:
   $\text{Average of two numbers} = \frac{\text{Sum of two numbers}}{2} = \frac{16}{2} = 8$

4. Verify and Summarize

We verified our calculations at each step, confirming the sums and averages based on the given information. The total calculations are accurate.

Final Answer

The average of the remaining two numbers is $\boxed{8}$.