The variance of 25 observations is 4. If 2 is added to each observation, then the new variance of the resulting observations is

Options

A. A. 2
B. B. 4
C. C. 6
D. D. 8

Answer

To solve the problem, we need to understand how variance behaves when a constant is added to each observation. Here’s a step-by-step solution:

### Step 1: Understand the concept of variance
Variance is a measure of how spread out the observations are in a dataset. It is calculated based on the average of the squared differences from the mean.

### Step 2: Identify the given information
We are given:
- The number of observations (n) = 25
- The variance of these observations (σ²) = 4

### Step 3: Analyze the effect of adding a constant
When a constant (in this case, 2) is added to each observation, the variance remains unchanged. This is because variance measures the spread of the data, and adding a constant shifts all data points equally without affecting their relative distances from the mean.

### Step 4: Calculate the new variance
Since adding a constant does not change the variance, the new variance after adding 2 to each observation will still be:
- New Variance = Old Variance = 4

### Conclusion
The new variance of the resulting observations is 4.