Question

Given below are two statements:
Statement I: Deflating procedure can be used for retaining continuity in the comparison between two or more index series.
Statement II: The sum of squared deviations is the least when taken from the mean.
In light of the above statements, choose the most appropriate answer:

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is correct but Statement II is false
• D. Statement I is incorrect but Statement II is true

Hint:

Remember the two main AM properties for exams:
1. The sum of deviations from the mean is zero: \( \sum(x - \bar{x}) = 0 \).
2. The sum of squares of deviations from the mean is minimum.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question covers properties of statistical indices and a fundamental property of the Arithmetic Mean.

Step 3: Detailed Explanation:
Statement I analysis: Deflating is a statistical process used to adjust a value (like GDP or a price index) for inflation, allowing for a consistent comparison of data over time or between different series. It helps maintain continuity in trend analysis. This statement is true.
Statement II analysis: This is a fundamental property of the Arithmetic Mean.
Mathematically, for a set of data \( x_i \):
\[ \sum (x_i - A)^2 \text{ is minimum when } A = \text{Mean } (\bar{x}) \]
Any value other than the mean will yield a higher sum of squared deviations. This statement is true.

Step 4: Final Answer:
Both Statement I and Statement II are factually and mathematically correct.