1. Measure of precision
- Probability curve shows the relationship between the size of an error and the probability of its occurrence. It provides the most accurate method for studying the precision of surveys.
- It provides the best available means of estimating the precision of future planned surveys.

2. How it can be measured?
- calculate the most probable value:
:is the most probable value of the quantity
:the sum of the individual measurements (M).
n: the total number of observations.

3. - calculate the residual:
v: is the residual in any observation.
Note that the width of the probability curve can be used as an indication of the relative precision of the observations.

4. Statistical term more commonly used to express precisions of groups of observations is standard deviation:
Where:
: is the sum of the squares of the residual.
- The area between residuals of +σ and –σ equals 68.3 percent of the total area under the probability curve.

5. The 50, 90, and 95 percent errors:
The probability of an error of any percentage can be determined by the following equation:
Ep=Cpσ
Where:
Ep is a certain percintage error;
Cp is a constant
σ is the standard error

6. E50= 0.67456 σ (probable error) E90= 1.6449 σ E95=1.9599 σ
Commonly used to specify precisions required in surveying projects

7. Example: Suppose that a line has been measured ten times using the same equipment and procedures. The results are shown in the table. It is assumed that no mistakes exist, and the observations have already been corrected for all systematic errors. Compute the most probable value for the line length, its standard deviation, and error having 50, 90 and 95 percent probability.