Given the variance of 30 observations is 20. if each of the observations is divided by 2, then new variance of the resulting oservations is

Options

A. 20
B. 10
C. 5
D. None of these

Answer

To find the new variance after dividing each observation by 2, we can follow these steps:

### Step 1: Understand the relationship between variance and scaling
When each observation in a dataset is multiplied or divided by a constant, the variance of the new dataset is affected by the square of that constant. Specifically, if you multiply each observation by a constant \( k \), the new variance becomes \( k^2 \times \text{(original variance)} \).

### Step 2: Identify the original variance
We are given that the variance of the original 30 observations is 20.

### Step 3: Determine the scaling factor
In this case, each observation is divided by 2. Therefore, the scaling factor \( k \) is \( \frac{1}{2} \).

### Step 4: Calculate the new variance
Using the relationship identified in Step 1, we can calculate the new variance:
\[ \text{New Variance} = \left(\frac{1}{2}\right)^2 \times \text{(original variance)} \]
Substituting the values:
\[ \text{New Variance} = \left(\frac{1}{2}\right)^2 \times 20 = \frac{1}{4} \times 20 = 5 \]

### Conclusion
The new variance of the resulting observations after dividing each by 2 is **5**.

---