Statistics

We have,

We know that




Arithmetic means

The correct answer is (D) : 252500.

Step 1: Understanding the Concept:
This problem relates the fundamental statistical measures: mean, standard deviation (or variance), and the sum of the squares of individual data points.

Step 2: Key Formula or Approach:
Use the computational formula for variance, which links all these quantities: Where: = standard deviation = sum of squares of all items (this is what we need to find) = total number of items = mean of the items Rearrange this formula to solve for .

Step 3: Detailed Explanation:
From the problem statement, we have the following values: Total number of items, Mean, Standard deviation, First, calculate the variance, which is the square of the standard deviation: Now, substitute the known values into the variance formula: Calculate the square of the mean: Now, solve for the unknown term : Add 2500 to both sides: Finally, to find the sum of all squares of the items ( ), multiply both sides by 100:

Step 4: Final Answer:
The sum of all squares of the items is 251600.