ERRORS AND STATISTICS Flashcards
Entails the entire process of obtaining a desired quantity, including preparations (instrument calibration and setup), pointing, matching, and comparing
Measurement
Process of determining the extent, size or dimensions of a particular quantity in comparison to a given standard
Measurement
Consists of several physical operations which renders numerical value
Measurement
Measurements are numerical values for random variables which are subject to
statistical fluctuations
due to observational errors
Statistical variations
refers to the difference between the measured or calculated value of a quantity and a given or established (true) value of that quantity
ERROR
Formula for error
refers to the difference between the measured or
calculated value of a quantity and a given or established
(true) value of that quantity
Formula for error
𝜺 = 𝒙 − 𝝉
negative of error
Correction
Formula of Correction
𝐂𝐨𝐫𝐫𝐞𝐜𝐭𝐢𝐨𝐧 = − (𝒙 − 𝝉)
SOURCES OF ERRORS
Natural Errors
Instrumental Errors
Personal Errors
Occurs due to variations of natural phenomena such as changes in temperature, humidity, wind velocity, magnetic declination, refraction, etc.
Natural Errors
Arises due to imperfections or faulty adjustment of instruments.
Instrumental Errors
Arises principally due to limitations of the senses of sights, touch and hearing of the observer.
Personal Errors
Types of Errors
Mistake or blunders
Systematic Errors
Random/Accidental Errors
Occurs due to lack of experience, carelessness, poor judgement, confusion in the observations
If the mistake remain undetected, it may produce
serious effect on the whole work
Mistake or blunders
Common Mistakes/blunders
➢ Reading the wrong graduation on the tape
➢ Omitting a whole length of tape
➢ Reading a scale backward
➢ Sighting the wrong target
➢ Incorrect recording of field notes
➢ Transposition of figures
➢ Misplacing a decimal point
is a cumulative error that occur under the same conditions.
Systematic Errors
Caused by physical and natural conditions that vary in accordance with known mathematical or physical laws.
Systematic Errors
Common Systematic Errors
➢ Equipment out of calibration
➢ Personal biases of the observer
➢ Use of incorrect units (feet instead of meters)
Produced by irregular causes that are beyond the control of the observer
Random/Accidental Errors
This variation results from observational errors which have known functional relationship based upon deterministic system
Random/Accidental Errors
Refers to the degree of agreement/consistency between several measurements of a quantity.
Precision
It is a measure of uniformity of the outcome/result
Precision
Refers to the degree of conformity/closeness of a measured value with the absolute/true value of the quantity.
Accuracy
General Uses of Statistics
Statistics aids in decision making
❑ Provides comparison
❑ Explains action that has taken place
❑ Justifies a claim or assertion
❑ Predicts future outcome
❑ Estimates unknown quantities
Statistics summarizes data for public use
MEASURES OF CENTRAL TENDENCY
➢ Mean
➢ Median
➢ Midrange
➢ Mode
Sum of all the values of the observations divided by the number of observations
Sample Mean
Most Probable Value (MPV)
Sample Mean
Most familiar measure of central tendency used
Sample Mean
positional middle of the arrayed data
Sample Median
Value of observation that is midway along the range
Midrange
Value that occurs most frequently in the sample
Sample Mode
The total spread of the sample
Range
Parameter of dispersion or spread
Variance
Defined as the positive square root of the variance
Standard Deviation
Refers to the ratio of the error to the measured or estimated quantity
Relative Error/Precision
Refers to the ratio between the total error and the total length of the survey.
Ratio of Misclosure
