Average of 12 numbers is 14. If each number is doubled, then what will be the new average?

Options

A. 28
B. 18
C. 20
D. 24

Answer

To solve the problem step by step, let's follow the reasoning outlined in the video transcript.

### Step 1: Understand the average formula
The average (mean) of a set of numbers is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of terms}} \]

### Step 2: Calculate the sum of the 12 numbers
Given that the average of 12 numbers is 14, we can find the sum of these numbers using the formula:
\[ \text{Sum} = \text{Average} \times \text{Number of terms} \]
Substituting the values:
\[ \text{Sum} = 14 \times 12 = 168 \]

### Step 3: Determine the new sum after doubling each number
If each of the 12 numbers is doubled, the new sum will also be doubled. Therefore:
\[ \text{New Sum} = 2 \times \text{Original Sum} = 2 \times 168 = 336 \]

### Step 4: Calculate the new average
Now, we can find the new average using the same average formula:
\[ \text{New Average} = \frac{\text{New Sum}}{\text{Number of terms}} \]
Substituting the values:
\[ \text{New Average} = \frac{336}{12} \]

### Step 5: Simplify to find the new average
Now, we simplify:
\[ \text{New Average} = 28 \]

### Conclusion
The new average after doubling each of the 12 numbers is **28**.

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