Module 3

• Measurement - A direct or indirect process of determining the extent, size or dimensions of a quantity in comparison to a given standard.
• Observation - is a single, unadjusted determination of a linear or angular value
• Measurements are numerical values for random variables which are subject to statistical fluctuations
• Statistical variations is an inherent quality of physical properties attributed to observational errors
• In 1983, the Philippines adopted the Metric System or SI (International System), as its official system of measurements, phasing out the English System.
• In the Philippines, angular measurements are expressed using the Sexagesimal System
• 180 degrees = pi x radians
• Error - The difference between the measured or calculated value of a quantity and given or established (“true”) value of that quantity
• E = X – t
• Correction - The negative of error
• Correction =  t – X
• Natural Errors - Caused by variations in the phenomena of nature such as changes in magnetic declination, temperature, refraction, and the like.
• Instrumental 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 sight, touch

  and hearing of the observer
• Mistakes or Blunders - Actually not errors because they are usually so gross in magnitude

  compared to the other types of errors
• Mistakes or Blunders - Actually not errors because they are usually so gross in magnitude compared to the other types of errors
• Systematic or Cumulative Errors - Caused by physical and natural conditions that vary in accordance with known mathematical or physical laws
• Random or Accidental Errors - Produced by irregular causes that are beyond the control of the

  Observer
• Common Mistake - Reading the wrong graduation on the tape
• Common Mistake - Misplacing a decimal point
• Common Systematic Errors - Equipment out of calibration
• Precision - degree of refinement and consistency of the performance of an operation used to obtain the result and measure of uniformity or reproducibility of the result
• Accuracy - degree of conformity with a standard or accepted value
• Most Probable Value - Sum of all the values of the observations divided by the number of observations
• Sample Median - Positional middle of the arrayed data
• Sample Midrange - Value of observation that is midway along the range
• Sample Midrange - Arithmetic mean of the largest and smallest observations
• Sample Mode - Value that occurs most frequently in the sample
• Range – total spread of the sample
• Range = Largest value - Smallest value
• Variance - Parameter of dispersion or spread
• Standard Deviation - Defined as the positive square root of the variance
• Relative Error – or Precision refers to the ratio of the error to the measured or estimated quantity
• Ratio of Misclosure - the ratio between the total error and the total length of the survey
• Probable Error - A quantity which, when added to and subtracted from the MPV, defines a range within which there is 50% chance that the true value lies inside (or outside) the limits
• Probable Error - A logical estimate of the measured quantity
• 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