The mean of 100 numbers observations is 50 and their standards deviation is 5. The sum of all squares of all the observations is (a)50,000          (b) 250,000         (c) 252500         (d) 255000

Explanation

To find the sum of all squares of the observations, we can use the relationship between the mean, variance, and the sum of squares. Here’s a step-by-step solution:

### Step 1: Understand the given information
- Mean (\( \bar{x} \)) = 50
- Number of observations (n) = 100
- Standard deviation (\( \sigma \)) = 5

### Step 2: Calculate the variance
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