Question

The method of least squares is used to:

• A. Eliminate systematic errors
• B. Reduce random errors
• C. Increase gross errors
• D. Correct instrumental errors

Hint:

Always remember:
- Systematic errors are "corrected".
- Random errors are "adjusted" (using Least Squares).
- Gross errors are "eliminated".

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Errors in surveying observations are classified into three types:
1. Gross Errors (Blunders): Human mistakes (e.g., misreading a tape). They must be detected and removed.
2. Systematic Errors: Errors that follow a fixed pattern or mathematical law (e.g., tape expansion due to heat). They are corrected using formulas.
3. Random Errors (Accidental): Unpredictable variations that remain after gross and systematic errors are accounted for. They follow the laws of probability.
Step 2: Key Formula or Approach:
The Principle of Least Squares states that the "most probable value" of a quantity is the one for which the sum of the squares of the residuals (errors) is a minimum.
\[ \sum v_i^2 \rightarrow \text{minimum} \]
Step 3: Detailed Explanation:
Since random errors cannot be eliminated, we use statistical methods to distribute them such that the overall discrepancy in the network is minimized. The method of least squares provides a mathematically rigorous way to find the best estimate from redundant observations, thereby reducing the influence of random errors.
Step 4: Final Answer:
The method of least squares is primarily used to adjust observations and reduce random errors.