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General Surveying > [PPT2] Errors and Statics > Flashcards

[PPT2] Errors and Statics Flashcards

1
Q

MEASUREMENT

A
  • Used alternatively with observation
  • Observations made to determine unknown
    quantities
  • A numerical value as a result of some physical
    operations such as preparation, pointing, matching, & comparing
  • May be classified as:
    – Direct: to determine distances and angles
    – Indirect: to compute for the station coordinates
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2
Q

ERROR AND CORRECTION

A

Error - refers to the difference between a given measurement and the “true” or “exact” value of the measured quantity
Correction - the negative of error

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3
Q

MEASUREMENT AND ERROR

A

It can be stated unconditionally that:
* no measurement is exact,
* every measurement contains errors
* the true value of a measurement is never known, thus
* the exact sizes of the errors present are always unknown

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4
Q

REPEATED MEASUREMENTS

A

PROBLEM: Variability
* An inherent quality of physical properties
* Must be accepted as a basic property of observations
* Measurements are numerical values for random variables which are subject to statistical fluctuations
* Statistical variations are due to observational errors

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5
Q

SOURCES OF ERRORS

(NIP)

A

1. Natural errors – Caused by variations in the phenomena of nature such as changes in magnetic declination, temperature, refraction, atmospheric pressure, etc.
2. Instrumental errors – Due to imperfections in the instruments used, either from faults in construction or improper adjustments (e.g., divisions not uniformly spaced)
3. Personal errors – Arise due to limitations of the human senses (e.g., ability to read a micrometer or to center a level bubble). Magnitude are affected by the personal ability to see and by manual dexterity

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6
Q

TYPES OF ERRORS

(MSR)

A
  1. Mistake or Blunders
  2. Systematic Errors
  3. Random Errors
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7
Q

1. MISTAKE OR BLUNDERS

A
  • Actually not errors because they are usually so
    gross in magnitude compared to the other types of errors
  • One of the most common reasons is simple carelessness on the part of the observer
  • An observation with a mistake is not useful unless the mistake is removed
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8
Q

COMMON MISTAKES

(ROTRMIS)

A
  1. Reading the wrong graduation on the tape
  2. Omitting a whole length of tape
  3. Transposition of figures
  4. Reading a scale backward
  5. Misplacing a decimal point
  6. Incorrect recording of field notes
  7. Sighting the wrong target
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9
Q

2. SYSTEMATIC ERROR

A
  • So called because they occur according to some deterministic system which, when known, can be expressed by some functional relationship
  • Also called a cumulative error
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10
Q

TYPES OF SYSTEMATIC ERROR

A

a. Constant Error – if its magnitude and sign remains the same throughout the measuring process. e.g. tape “too short” or “too long”
b. Counteracting – if its sign changes while its magnitude remains the same. Perhaps due to personal bias of the observer

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11
Q

3. RANDOM ERROR

A
  • This variation results from observational errors which have no known functional relationship based upon a deterministic system.
  • These errors which exhibits random behavior must be treated accordingly.
  • Whereas systematic variations are dealt with mathematically using functional relationships or models, random variables must use probability models
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12
Q

CONCETS AND TOPICS
IN STATISTICS

A

A. General Uses of Statistics
B. Precision versus Accuracy
C. The Concept of Probability
D. Measures of Central Tendency
E. Sample Statistics for Dispersion
F. Measures of Quality

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13
Q

A. GENERAL USES OF STATISTICS

A
  • 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
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14
Q

B. PRECISION AND ACCURACY

A

Precision - degree of refinement with which a quantity is measured

Accuracy - denotes how close a given measurement is
to the true value of the quantity

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15
Q

C. THE CONCEPT OF PROBABILITY

(RPR)

A

Random Event – is one whose relative frequency of
occurrence approaches a stable limit as the number of observations/repetitions of an experiment is increased to infinity.

Probability – is the likelihood associated with a random event.

Random Variable – defined as a variable that takes on any of several possible values, with each of which is associated a probability

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16
Q

REPRESENTATIONS OF THE PROBABILITY DENSITY

A

Frequency Diagrams
* Histogram – constructed to represent the probability density of a single random variable. Bar graphs that show the frequency distributions in the data.
* Stereogram – constructed to represent the probability density of two random variables.

17
Q

MEASURES OF CENTRAL TENDENCY

A
  1. Median
  2. Mean
  3. Mode
  4. Midrange
18
Q

1. SAMPLE MEDIAN

A
  • positional middle of the arrayed data.

Characteristics:
* Affected by the position of each item but not by the value of each item.
* A stable measure of central tendency.
* For even-numbered data set, median is the average of the 2 items in the middle.
* The number of observations larger than the median equals the number smaller than the median.

19
Q

2. SAMPLE MEAN

A
  • Sum of all the values of the observations divided by the number of observations
  • Most Probable Value; robust and more manipulable

Characteristics:
* Most familiar measure of central tendency used.
* Affected by the value of every observation.
* In particular, it is strongly influenced by extreme values.
* Since it is a calculated number, it may not be an actual number in the data set

20
Q

3. SAMPLE MODE

A
  • Value that occurs most frequently in the sample

Characteristics:
* Not always exist. If it does, it may not be unique (2 or more sample modes).
* Not affected by extreme values
* Easiest to compute

21
Q

4. MIDRANGE

A
  • value of observation that is midway along the range
  • arithmetic mean of the largest and smallest observations
22
Q

E. SAMPLE STATISTICS FOR DISPERSION

(RMVS)

A

1. Range
– the total spread of the sample
– Largest value-Smallest value
2. Mean Deviation
– arithmetic mean of the absolute values of the deviation from any measure of position (usually the mean).
3. Variance
– parameter of dispersion or spread
4. Standard Deviation
– defined as the positive square root of the variance

23
Q

F. MEASURES OF QUALITY

A
  • Weight – defined as the quantity that is inversely proportional to variance.
  • Relative Precision – refers to the ratio of the measure of precision to the quantity being measured or estimated.
  • Mean Square Error – used as a measure of accuracy
24
Q

I. RESIDUAL

A
  • Sometimes called the deviation
  • Defined as the difference between any measured quantity and its most probable value
25
Q

RESIDUAL VS. ERROR

A
  • Error is frequently used when residual is meant
  • Residual has the same sense as the “correction” which is the negative of error
  • Error is a hypothetical concept while residual does have value in the reduction of redundant observational data

Error
* Negative of correction
* Indeterminate
* Theoretical concept
* When population is used

Residual
* Same sense as the correction
* Takes a particular value
* Not a hypothetical concept
* When sample set is used

26
Q

II. PROBABLE ERROR

A
  • 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 thus, set
  • A logical estimate based upon:
    – methods and equipment used
    – experience of the observers
    – field conditions existing during the measurement
27
Q

III. INTER-RELATIONSHIP OF ERRORS

A
  • Since all quantities measured directly contain errors, any values computed from them will also contain errors
  • Error propagation
    – Intrusion (propagation) of errors that occur in quantities computed from direct measurements
    – Examples include the sum and product of the probable errors
28
Q

IV. RELATIVE PRECISION

A
  • Expressed by a fraction having the magnitude of the error in the numerator and the magnitude of a measured quantity in the denominator
  • Used to define degree of refinement obtained
  • Both quantities should be in the same units and the numerator is reduced to 1 to provide easy comparison with other measurements
29
Q

V. WEIGHTED OBSERVATIONS

A
  • Surveying data must usually conform to a given set of geometric conditions
  • If not, measurements are adjusted to force that geometric closure
  • Weight of an observation is a measure of its relative worth compared to other measurements
  • For a set of uncorrelated observations,
    – ↑ Precision, ↓ Variance, ↓ correction
    – i.e., weights are inversely proportional to variances
    – Correction sizes should be inversely proportional to weights
  • Weights can also be assigned using:
    – Judgement of the surveyor (a priori)
    – number of measurements taken for a particular quantity
    – the assumption that it is inversely proportional to the square of the probable error
    – Inverse of lengths and number of setups for differential leveling lines

General Surveying (5 decks)

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