In surveying and observations, which statements correctly describe accidental (random) errors in measurements?

Introduction / Context:
Every measurement contains error. In surveying and geodesy, it is essential to distinguish between systematic errors (bias) and accidental or random errors to ensure correct data adjustment and quality control. Understanding the behavior of accidental errors guides the use of statistical methods for precision estimation.

Given Data / Assumptions:

• Accidental errors arise from small, uncontrollable variations in observation conditions and human/ instrument limitations.
• They vary in sign and magnitude and tend to cancel out over many observations.
• We consider standard field conditions without gross mistakes (blunders).

Concept / Approach:
Systematic errors can be modeled and corrected. Accidental errors, however, cannot be eliminated by deterministic corrections and are evaluated statistically (mean, variance). In classical surveying pedagogy they are often termed ‘‘compensating errors’’ because positive and negative deviations tend to offset each other over repeated measurements.

Step-by-Step Solution:
Recognize that accidental errors arise unpredictably → not removable by fixed correction.Their magnitudes are typically small compared to systematic effects in well-run observations.Because signs vary, multiple observations reduce their effect on the mean (hence ‘‘compensating’’).

Verification / Alternative check:
Least-squares adjustment theory treats residuals as random; precision improves with the square root of the number of observations, indicating compensatory behavior.

Why Other Options Are Wrong:

• Each individual statement characterizes accidental errors in standard textbooks; therefore the combined choice ‘‘all the above’’ is appropriate.

Common Pitfalls:

• Confusing accidental errors with systematic bias (which can be modeled and corrected).
• Assuming a single reading is ‘‘true’’; precision demands repetition and averaging.

Final Answer:
all the above