Module 3 | Measurements, Errors, and Basic Statistics

Entails the entire process of obtaining a desired quantity, including: preparations (instrument calibration and setup), pointing, matching, comparing

It is a single, unadjusted determination of a linear or angular value

In conducting the process of measurement, it is necessary to define and use the proper ______ applicable for the quantity being observed.

The official system of measurements adopted by the Philippines in 1983, based on the 'meter' as the unit for linear measurements.

Measurements related to length or distance.

The fundamental unit of length in the metric system.

A unit of length in the metric system, equal to 0.01 meters.

A unit of length in the metric system, equal to 0.001 meters.

A unit of area in the metric system, equal to the area of a square with sides of 1 meter.

Measurements related to angles.

The system used in the Philippines for expressing angular measurements, where a circle is divided into 360 degrees, each degree is divided into 60 minutes, and each minute is further divided into 60 seconds.

A tool used for measuring angles.

A unit of angular measurement in the SI system.

A format for expressing angles in degrees, minutes, and seconds.

A unit of angular measurement in the centesimal system, where 100 grads equal 90 degrees.

The difference between the measured or calculated value of a quantity and given or established (“true”) value of that quantity

ɛ = X-τ

The negative of the error.

correction = τ-X

Source of errors caused by variations in the phenomena of nature such as changes in magnetic declination, temperature, refraction, and the like.

Source of errors due to imperfections in the instruments used, either from faults in construction or improper adjustments.

Arise principally from the limitations of the senses of the observer (sight, touch and hearing).

Type of Errors: Actually not errors because they are usually so gross in magnitude. Resulting usually from stupidity, ignorance, or carelessness.

Type of Errors: Errors caused by physical and natural conditions that vary according to known mathematical or physical laws.

Produced by irregular causes that are beyond the control of the observer.

The degree of refinement and consistency of the performance of an operation used to obtain a result.

Measure of uniformity or reproducibility of the result.

The degree of conformity with a standard or accepted value, indicating how close a given measurement is to the “true” value of the quantity.

The sum of all the values of the observations divided by the number of observations, representing the most familiar measure of central tendency.

x̄

The positional middle of the arrayed data. Affected by the position of each item but not by the value of each item and considered a stable measure of central tendency.

The value of the observation that is midway along the range, calculated as the arithmetic mean of the largest and smallest observations.

midrange = (maximum value + minimum value) / 2.

The value that occurs most frequently in the sample, not affected by extreme values and the easiest to compute.

The difference between the largest and smallest values in a set of data.

range = max - min

A parameter of dispersion or spread, calculated as the average of the squared differences from the mean.

σ²

The positive square root of the variance.

A measure of how spread out data is from the mean. It quantifies the amount of variation or dispersion in a set of values.

σ

The ratio between the total error and the total length of the survey.

The value that is most likely to occur in a set of measurements.

The difference between any measured quantity and its Most Probable Value (MPV).

A quantity that defines a range within which there is a 50% chance that the true value lies inside or outside the limits.

Expressed as a fraction, it represents the magnitude of the error compared to the magnitude of a measured quantity.

An inherent quality of physical properties attributed to observational errors.

1 inch = _____ cm

1 yard = _____ m

1 acre = _____ m²

1 hectare = _____ m²

Positive angles are measured in _____ direction.

Negative angles are measured in _____ direction.