Lesson 2: Errors and Statistics Flashcards
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 a numerical value.
Measurement
Maybe direct or indirect
Measurement
It entails the entire process of
obtaining a desired quantity, including
preparations (instrument calibration and
setup), pointing, matching, and comparing.
Measurement
is a single, unadjusted
determination of a linear or angular value.
Observation
Measurements are numerical values for
random variables which are subject to
statistical fluctuations.
Variability in Repeated
Measurements
An inherent quality of physical properties.
Variability in Repeated
Measurements
Statistical variations due to observational
errors.
Variability in Repeated
Measurements
difference between the measured or
calculated value of a quantity and given or
established (“true”) value of that quantity.
Error
the negative of error.
Correction
Sources of Errors
- Natural Errors
- Instrumental Errors
- Personal Errors
caused by variations in
the phenomena of nature, such as
changes in magnetic declination,
temperature, etc.
Natural Errors
due to imperfections in the instruments used.
Instrumental Errors
arise principally from
the limitations of the senses of sight,
touch, and hearing of the observer.
Personal Errors
Types of Errors
- Mistakes or Blunders
- Systematic or Cumulative Errors
- Random or Accidental Errors
Mistakes or Blunders
- Actually not errors because they are
usually so gross in magnitude compared to
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.
Common Mistakes or Blunders
- Reading the wrong graduation on the tape.
- Omitting a whole length of tape.
- Transposition of figures.
- Misplacing a decimal point.
- Incorrect recording of field notes.
- Sighting the wrong target.
So-called because they occur according to
some deterministic system, which, when
known, can be expressed by some
functional relationship.
Systematic or Cumulative Errors
Caused by physical and natural conditions
that vary in accordance with known
mathematical or physical laws.
Systematic or Cumulative Errors
Types Systematic Error
- Constant Error
- Counteracting
if its magnitude and sign
remains the same throughout the
measuring process or field conditions are
unchanged.
Constant Error
if its sign changes while its
magnitude remains the same.
– due to the personal bias of the observer.
Counteracting
Common Systematic or
Cumulative 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 or Accidental Errors
This variation results from observational
errors which have no known functional
relationship based upon a deterministic
system.
Random or Accidental Errors
Must use probability models.
Random or Accidental Errors
General Uses of Statistics
- Statistics aid in decision making.
- Statistics summarizes data for public use.
Statistics aid in decision making.
– Provides comparison.
– Explains action that has taken place.
– Justifies a claim or assertion.
– Predicts future outcome.
– Estimates unknown quantities.
degree of refinement and measure
of the uniformity of the result.
Precision
- degree of conformity with a
standard or accepted value. - denotes how close a given measurement is
to the absolute value of the quantity.
Accuracy
The Concept of Probability
- Probability
- Random Variable
- Random Event
is the likelihood associated
with a random event.
Probability
a variable that takes on
any of several possible values.
Random Variable
is one whose relative
frequency of occurrence approaches a
stable limit as the number of observations
is increased to infinity.
Random Event
represents the probability
density of a single random variable.
Histogram
represents the probability
density of two random variables.
Stereogram
Measures of Central Tendency
- Median
- Mean
- Mode
- Midrange
positional middle of the
arrayed data.
Sample median
Characteristics of sample median
- Affected by the position of each item but not by the value of each item.
- A stable measure of central tendency.
sum of all the values of the
observations divided by the number of
observations. (Most Probable Value)
Sample mean
Characteristics of sample mean
- 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.
value that occurs most
frequently in the sample
Sample Mode
Characteristics of sample mode
- Not always exist. If it does, it may not be
unique (2 or more sample modes). - Not affected by extreme values.
- Easiest to compute.
- value of observation that is
midway along the range. - arithmetic mean of the largest and
smallest observations.
Midrange
Sample Statistics for Dispersion
- Range
- Mean Deviation
- Variance
- Standard Deviation
The total spread of the sample.
Range
arithmetic mean of the absolute values of
the deviation from any measure of
position.
Mean Deviation
Parameter of dispersion or spread.
Variance
Positive square root
of the variance
Standard Deviation
Measures of Quality
Weight
Relative Error or Precision
Ratio of Misclosure
the quantity that is inversely
proportional to variance.
Weight
ratio of the error to the measured or estimated quantity.
Relative Error or Precision
ratio between the total error and the total length of the survey.
Ratio of Misclosure
Sometimes called the deviation.
Residual
Defined as the difference between any
measured quantity and its most probable
value (MPV).
Residual
