2: Surveying Measurements

Measurement

* process of determining the extent, size, or dimensions of a particular quantity in comparison to a given standard
* consists of several physical operations which renders a numerical value
* may be direct or indirect

Observation

a single, unadjusted determination of a linear/angular value

Error

It is the difference between the true value and the measured value of a quantity.

Accuracy

It refers to the closeness of the measured value to the true value.

Precision

It refers to the closeness of two or more measured value to each other.

Natural error

caused of constant change in weather condition, refraction, and effect of gravity, temperature, and other laws of nature

Instrumental error

This error is due to defective production or failure to recalibrate the equipment

Human error

caused by the inability of an individual to make an exact observations due to the limitations of human sight, touch, and hearing

Gross error

They are blinders/mistakes in measurements which occur because some aspect of a surveying operation is performed by the geodetic engineer with carelessness, poor judgment, and improper execution or lack of attention

Systematic error

They can be constant or variable throughout an operation and are generally attributable to known circumstances

Random error

They are those variants which remain after all other errors have been removed. They are beyond the control of the observer and result from the human inability of the observer to make exact measurements

Probability

the likelihood associated with a random event

Random variable

a variable that takes on any of several possible values

Random event

is one whose relative frequency of occurrences approaches a stable limit as the number of observations is increased to infinity

Sample median

positional middle of the arrayed data

Sample mean

sum of all the values of the observations divided by the number of observations (most probable value)

Sample mode

value that occurs most frequently in the sample

Range

the total spread of the sample

Mean deviation

arithmetic mean of the absolute values of the deviation from any measure of position

Variance

parameter of dispersion or spread

Standard deviation

positive square root of the variance

Standard error

The curve also shows that the positive and negative errors are equal in size and frequency

Standard Normal Distribution

If each data value of a normally distributed random variable *x* is transformed into a z-score, the result will be this.

Relative Error

Expressed by a fraction having the magnitude of the error in the numerator and the magnitude of a measured quantity in the denominator

Weight

inversely proportional to the square of the corresponding probable errors