Module 3 | Measurements, Errors, and Basic Statistics

Measurement

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

Observation

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

Unit of measure

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

Metric/SI System

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

Linear Measurements

Measurements related to length or distance.

Meter (m)

The fundamental unit of length in the metric system.

Centimeter (cm)

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

Millimeter (mm)

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.

Angular Measurements

Measurements related to angles.

Sexagesimal System

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.

Protractor

A tool used for measuring angles.

Radian

A unit of angular measurement in the SI system.

Degrees-Minutes-Seconds (DMS)

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

Grads

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

Error

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

ɛ = X-τ

Correction

The negative of the error.

correction = τ-X

Natural Errors

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

Instrumental Errors

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

Personal Errors

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

Mistakes or Blunders

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

Systematic or Cumulative Errors

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

Random or Accidental Errors

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

Precision

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.

Accuracy

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

Sample Mean

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

x̄

Sample Median

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.

Sample Midrange

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.

Sample Mode

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

Range

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

range = max - min

Variance

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

σ²

Standard Deviation

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

Ratio of Misclosure

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

Most Probable Value (MPV)

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

Residual

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

Probable Error

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

Relative Error/Precision

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

Statistical variations

An inherent quality of physical properties attributed to observational errors.

2.54

1 inch = _____ cm

0.9144

1 yard = _____ m

4046.8564

1 acre = _____ m²

10,000

1 hectare = _____ m²

Counterclockwise (anti-clockwise)

Positive angles are measured in _____ direction.

Clockwise

Negative angles are measured in _____ direction.