The variance of 20 observation is 5. If each observation is multiplied by 3, then what is the new variance of the resulting observation?

Options

A. 5
B. 10
C. 15
D. 45

Explanation

To find the new variance after multiplying each observation by 3, we can follow these steps:

### Step 1: Understand the formula for variance transformation
When each observation in a dataset is multiplied by a constant, the variance of the new dataset can be calculated using the formula:
\[ \text{New Variance} = \text{Old Variance} \times (\text{Constant})^2 \]

### Step 2: Identify the old variance and the constant
From the problem, we know:
- Old Variance = 5
- Constant = 3 (since each observation is multiplied by 3)

### Step 3: Calculate the square of the constant
Now, we need to calculate the square of the constant:
\[ (\text{Constant})^2 = 3^2 = 9 \]

### Step 4: Substitute the values into the formula
Now, we can substitute the values into the formula for the new variance:
\[ \text{New Variance} = 5 \times 9 \]

### Step 5: Perform the multiplication
Calculating the above expression:
\[ \text{New Variance} = 45 \]

### Conclusion
The new variance after multiplying each observation by 3 is:
\[ \text{New Variance} = 45 \]

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