Lesson 2: Errors and Statistics

Question 1

Process of determining the extent, size, or
dimensions of a particular quantity in
comparison to a given standard.

Answer 1

Measurement

Question 2

Consists of several physical operations
which renders a numerical value.

Answer 2

Measurement

Question 3

Maybe direct or indirect

Answer 3

Measurement

Question 4

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

Answer 4

Measurement

Question 5

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

Answer 5

Observation

Question 6

Measurements are numerical values for
random variables which are subject to
statistical fluctuations.

Answer 6

Variability in Repeated
Measurements

Question 7

An inherent quality of physical properties.

Answer 7

Variability in Repeated
Measurements

Question 8

Statistical variations due to observational
errors.

Answer 8

Variability in Repeated
Measurements

Question 9

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

Answer 9

Error

Question 10

the negative of error.

Answer 10

Correction

Question 11

Sources of Errors

Answer 11

• Natural Errors
• Instrumental Errors
• Personal Errors

Question 12

caused by variations in
the phenomena of nature, such as
changes in magnetic declination,
temperature, etc.

Answer 12

Natural Errors

Question 13

due to imperfections in the instruments used.

Answer 13

Instrumental Errors

Question 14

arise principally from
the limitations of the senses of sight,
touch, and hearing of the observer.

Answer 14

Personal Errors

Question 15

Types of Errors

Answer 15

1. Mistakes or Blunders
2. Systematic or Cumulative Errors
3. Random or Accidental Errors

Question 16

Mistakes or Blunders

Answer 16

• 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.

Question 17

Common Mistakes or Blunders

Answer 17

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

Question 18

So-called because they occur according to
some deterministic system, which, when
known, can be expressed by some
functional relationship.

Answer 18

Systematic or Cumulative Errors

Question 19

Caused by physical and natural conditions
that vary in accordance with known
mathematical or physical laws.

Answer 19

Systematic or Cumulative Errors

Question 20

Types Systematic Error

Answer 20

• Constant Error
• Counteracting

Question 21

if its magnitude and sign
remains the same throughout the
measuring process or field conditions are
unchanged.

Answer 21

Constant Error

Question 22

if its sign changes while its
magnitude remains the same.

– due to the personal bias of the observer.

Answer 22

Counteracting

Question 23

Common Systematic or
Cumulative Errors

Answer 23

1. Equipment out of calibration.
2. Personal biases of the observer.
3. Use of incorrect units (feet instead of meters)

Question 24

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

Answer 24

Random or Accidental Errors

Question 25

This variation results from observational errors which have no known functional relationship based upon a deterministic system.

Answer 25

Random or Accidental Errors

Question 26

Must use probability models.

Answer 26

Random or Accidental Errors

Question 27

General Uses of Statistics

Answer 27

* Statistics aid in decision making. * Statistics summarizes data for public use.

Question 28

Statistics aid in decision making.

Answer 28

– Provides comparison. – Explains action that has taken place. – Justifies a claim or assertion. – Predicts future outcome. – Estimates unknown quantities.

Question 29

degree of refinement and measure of the uniformity of the result.

Answer 29

Precision

Question 30

- degree of conformity with a standard or accepted value. - denotes how close a given measurement is to the absolute value of the quantity.

Answer 30

Accuracy

Question 31

The Concept of Probability

Answer 31

- Probability - Random Variable - Random Event

Question 32

is the likelihood associated with a random event.

Answer 32

Probability

Question 33

a variable that takes on any of several possible values.

Answer 33

Random Variable

Question 34

is one whose relative frequency of occurrence approaches a stable limit as the number of observations is increased to infinity.

Answer 34

Random Event

Question 35

represents the probability density of a single random variable.

Answer 35

Histogram

Question 36

represents the probability density of two random variables.

Answer 36

Stereogram

Question 37

Measures of Central Tendency

Answer 37

1. Median 2. Mean 3. Mode 4. Midrange

Question 38

positional middle of the arrayed data.

Answer 38

Sample median

Question 39

Characteristics of sample median

Answer 39

- Affected by the position of each item but not by the value of each item. - A stable measure of central tendency.

Question 40

sum of all the values of the observations divided by the number of observations. (Most Probable Value)

Answer 40

Sample mean

Question 41

Characteristics of sample mean

Answer 41

- 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.

Question 42

value that occurs most frequently in the sample

Answer 42

Sample Mode

Question 43

Characteristics of sample mode

Answer 43

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

Question 44

- value of observation that is midway along the range. - arithmetic mean of the largest and smallest observations.

Answer 44

Midrange

Question 45

Sample Statistics for Dispersion

Answer 45

1. Range 2. Mean Deviation 3. Variance 4. Standard Deviation

Question 46

The total spread of the sample.

Answer 46

Range

Question 47

arithmetic mean of the absolute values of the deviation from any measure of position.

Answer 47

Mean Deviation

Question 48

Parameter of dispersion or spread.

Answer 48

Variance

Question 49

Positive square root of the variance

Answer 49

Standard Deviation

Question 50

Measures of Quality

Answer 50

Weight Relative Error or Precision Ratio of Misclosure

Question 51

the quantity that is inversely proportional to variance.

Answer 51

Weight

Question 52

ratio of the error to the measured or estimated quantity.

Answer 52

Relative Error or Precision

Question 53

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

Answer 53

Ratio of Misclosure

Question 54

Sometimes called the deviation.

Answer 54

Residual

Question 55

Defined as the difference between any measured quantity and its most probable value (MPV).

Answer 55

Residual