The average of 12 numbers is 15 and the average of the first two numbers is 1(4) What is the average of the remaining numbers?

The correct option is 15.2.

To find the average of the remaining numbers, we can break the problem down step-by-step:

Step 1: Calculate the sum of all 12 numbers
The average of the 12 numbers is 15. Since the average is defined as the total sum divided by the count of numbers, we can find the sum by multiplying the average by the count of numbers:

$$\text{Total Sum}=\text{Average}\times \text{Total Count}$$

$$\text{Total Sum}=15\times 12=180$$

Step 2: Calculate the sum of the first two numbers
The average of the first two numbers is 14 (represented as 1(4) in the question). We find their sum by multiplying this average by 2:

$$\text{Sum of the first 2 numbers}=14\times 2=28$$

Step 3: Calculate the sum of the remaining numbers
Subtract the sum of the first two numbers from the total sum of all 12 numbers to get the sum of the remaining 10 numbers:

$$\text{Sum of the remaining 10 numbers}=180-28=152$$

Step 4: Calculate the average of the remaining numbers
Now, divide the sum of the remaining 10 numbers by 10 to find their average:

$$\text{Average of the remaining numbers}=\frac{152}{10}=15.2$$