Units and errors
Units
 SI units
 imperial units
 1" = 1 inch = 2.54 cm
 1' = 1 foot = 12 inches ≅ 30 cm
 1 mile ≅ 1.6 km
Probability basics and errors of measurements
Surveying is based on measurements of, usually, lengths and angles. It is important to understand errors, precision and accuracy.
If we make a measurement, we only find an approximation of the true value. We can get closer to the true value by
 conducting more advanced (more accurate) measurement,
 conducting more precise measurement or
 conducting more measurements,
and we still have only approximation of unknown value.
Precision
When we take distance by counting paces, we can not state the result at 4 significant digits.
If the distance from A to C is computed as distance AB + BC and BC was observed with poor precision or accuracy, the result AC has poor precision as well. Eg. if AB = 120 m, BC = 13.37 m, then the result should be 133 or 133.5 m. If AB = 120.00 m, BC = 13.37 m, it is justified to assume result distance is 133.37 m.
Coastline paradox
If the coastline of Great Britain is measured using fractal units 100 km long, then the length of the coastline is approximately 2,800 km. With 50 km units, the total length is approximately 3,400 km, approximately 600 km longer. More concretely, the length of the coastline depends on the method used to measure it (and can be even infinite).
Errors
We rather should write "Mistakes and errors" and we can divide them into a few kinds:
 Blunders
E.g. typo, misspeak, mishearing, improper use of equipment, lack of knowledge  Systematic errors
Usually can not be avoided: method chosen is imperfect, equipment is imperfect, influence of temperature, mechanical errors..  Random errors
Usually unavoidable small errors taken during observation often related to precision.One measurement can be slightly larger while the next is slightly smaller. Example of random errors is reading the value from ruler or using an improper force to stretch a tape.
Normal distribution
 parameter μ: mean (average) value of all values x_{0}, x_{1}, ... x_{n},
 parameter σ: standard deviation.
(1.1) μ = avg(x_{0}, x_{1}, ... x_{n}),
(1.2) σ_{n}^{2} = avg(Δ_{0}^{2}, Δ_{1}^{2}, ... Δ_{n}^{2}) = ∑ Δ_{i}^{2} / n, where
(1.3) Δ_{i} = x_{i}  x_{avg} is error of a particular value from its mean value.
Both σ and μ have the same units as original data measured. If we look at the graph above, we see that standard deviation determines the width of the distribution. The smaller deviation is, the smaller is the error of final value μ.
(1.4) SE(x_{avg}) = σ_{n1} / √n,
Above, n is the number of measurements and standard deviation is computed as
(1.5) σ_{n1}^{2} = ∑ Δ_{i}^{2} / (n  1).
Because we have only limited sample of measurements and because error (or deviation) on mere one sample is undefined, σ_{n1} formula slightly differs from (1.2) and provides better estimation. Around 67 % of samples are expected to belong to interval marked by the standard error. If standard error is widened to double, 95 % of samples fall into the interval.
Example
Let us say that our 5 teams conducted a survey and values of distance measured are x = { 1534 m, 1423 m, 1671 m, 1637 m, 1417 m }. Mean value μ is 1536.4 m, ∑ Δ_{i}^{2} = 55,369 m^{2}, σ_{n1} = 117.6 m, SE = 52.6 m. We can write that distance measured is 1536.4 m ± 52.6 m. Considering poor accuracy, there is no justification to use so many digits and the result should be written as 1540 m ± 50 m.
Adding up errors
The errors are random, some of them negative, other positive. If there are more random errors, they have a tendency to cancel each other.

If a distance from A to B is measured as several separate measurements of distances X_{0}, X_{1}, ... X_{n} whose sum determines the distance A to B, then error distance A to B is not sum of errors, but SE_{AB} = √n SE_{1}, where SE_{1} is an error of one measurement. If the error of measurement is 1 cm and we have 4 measurements to collect final distance, then final error is expected at 2 cm.
The errors are random, some of them negative, other positive. If there are more random errors, they have a tendency to cancel each other.

The formula above is simplification of adding up errors of measured values. When two or more measured values are added, the uncertainty associated with the sum is computed by taking the sum of the squares of the uncertainty associated with each measured value, and then taking the square root of the sum. This process is called summing in quadrature.
For example if x = 3.0 ± 1.0 and y = 11.0 ± 0.5, the expected result x + y = avg(x, y) ± SE_{result} = 14.0 ± 1.1, where SE_{result} = √(1.0^{2} + 0.5^{2}) = 1.1
Field notes
The topic is included here because improper recording in a field will most likely cause errors which can be very expensive. At least most important rules:
 Sketches should be labeled including approximate north direction. Put down time, place and crew on every paper.
 Each survey shall start on its page.
 There must be no doubt about any value. Don't correct values. Incorrect value shall be lined out and new value put instead.
 All values should be checked during recording.
 Never destroy original field record. Original record is often the only remedy to recover from a mistake.
 It is a good idea to put down also weather, condition. Snapshots taken by camera can be helpful too.