Mistakes and Errors in Surveying

In surveying, measurements can have unintended deviations. Some of these come from observer blunders called mistakes, while others are inherent in measurement and are called errors. Below we define both, explain their types, and highlight how they differ.

1. Mistakes (Observer Blunders)

Mistakes, or observer blunders, are caused by human factors like misunderstanding the problem, carelessness, fatigue, missed communication, or poor judgment. These are not measurement errors but avoidable slip‑ups. They are not because of human limitations of sight, hearing etc.

Examples of Mistakes

Recording 73.96 instead of 79.36 (number transposition)
Reading an angle counterclockwise but noting it as clockwise
Sighting the wrong target
Recording 682.38 instead of 862.38

Large mistakes must be detected through careful and systematic checking of all work. They are eliminated by repeating some or all measurements. Small mistakes blend into measurement errors and are hard to spot, so unchecked they may be treated as errors.

2. Errors in Surveying

After removing mistakes, remaining deviations are called errors. Errors are of two types: systematic and random.

2.1 Systematic Errors

Systematic errors, or biases, come from the measuring system. This includes:

The environment (temperature, wind, humidity)
The instrument (steel tape, level rod)
The observer (Due to Human limitations of Sight, hearing, etc.)

Systematic errors split into:

Constant Systematic Errors: Conditions stay constant. For example, a 100 ft tape always 0.02 ft too long generates the same +0.02 ft error. Apply one fixed correction (–0.02 ft) to all readings.
Variable Systematic Errors: Conditions change. For example, tape length changes with temperature (+0.005 ft when hot, –0.003 ft when cool). Measure the factor (temperature) each time and compute a new correction.

A calibrated 100 ft tape 0.02 ft too long: constant +0.02 ft error, corrected by –0.02 ft.
Hot‑day tape expansion of +0.005 ft vs cool‑day shrinkage of –0.003 ft: correct each reading with a temperature formula.

2.2 Random Errors

Random errors are unpredictable deviations remaining after removing mistakes and systematic errors. They come from small, uncontrollable factors and follow probability laws, so they are also called accidental errors.

We estimate random errors using least squares adjustment. In many observations, some readings err high and others low, so these deviations tend to cancel out.

For example, estimating to hundredths on a tape graduated to tenths may yield slightly high guesses and slightly low guesses. Over a series, they balance out.

Some observers consistently interpolate high.
Others consistently interpolate low.
Many favor certain digits, like 7 or 0.

3. Key Differences

Origin: Mistakes arise from human blunders; errors arise from measurement process.
Predictability: Mistakes are accidental and avoidable; systematic errors are predictable, random errors are probabilistic.
Correction: Mistakes require re‑measurement; systematic errors need mathematical corrections; random errors are estimated statistically.
Detection: Mistakes detected by checking work; systematic errors modeled by known laws; random errors inferred via statistical adjustment.

Theory of Errors in Observations