1What is measurement?
A process that involves observation and is subject to variation
2What is often used synonymously with measurement?
Observation
3Why can no observation be repeated exactly?
Because measurement is a process subject to variation
4What does variation in measurement imply about a measured quantity?
It cannot be completely determined
5What is the true value of a quantity considered in measurement?
An estimate, since the true value cannot be completely determined
6What is an error?
The expected difference between a measured value and the true value
7If τ denotes the true value and χ the observed value, what is the error ε?
ε = χ − τ
8Why can the exact value of error ε never be known?
Because the true value τ is never known
9What symbol denotes a good estimate of the true value?
χ̂
10What is a residual?
The difference between a good estimate of the true value and the observed value
11What is the formula for the residual v?
v = χ̂ − χ
12What quantity is actually used to express variation in a measurement?
The residual
13What are the three sources of errors?
Natural or physical, instrumental, and personal
14What is an example of a natural or physical source of error?
Settlement of the instrument over a station
15What is another example of a natural or physical source of error?
Unequal atmospheric refraction
16What is an example of an instrumental source of error?
Line of sight is not normal to the plumbline
17What is an example of a personal source of error?
Not centering the bubble exactly on a rod or pole
18What is another example of a personal source of error?
Parallax
19What are the three types of errors?
Gross errors, systematic errors, and random errors
20What are gross errors?
Blunders or mistakes
21What is an example of a gross error?
Recording 12.21 m instead of 12.12 m
22What are systematic errors?
Errors that occur according to a deterministic system and follow a pattern
23When can a systematic error be called a constant error?
When its magnitude and sign remain throughout the measurement
24What are random errors?
Errors that behave randomly and remain after gross and systematic errors are removed
25How are random errors dealt with?
Using probability models
26What causes whatever variation remains after removing gross and systematic errors?
Random errors
27What is a frequency distribution?
The basis for constructing a probability model for measurements
28What is a histogram?
A representation of the relative frequency of occurrence of measurements
29What is a class interval?
A range or interval used to group measurements in a frequency distribution
30What is frequency?
The number of measurements occurring at a particular value or interval
31What is probability?
The limiting value of the relative frequency
32What can be used instead of a histogram?
A probability distribution
33How is probability represented under a continuous curve?
By the area under the curve
34What is the curve representing the probability distribution called?
The probability density function
35What does the probability density function represent?
The random variable that represents the measurement
36What does μ represent in a probability distribution?
The central value or mean value of the measurement
37What are parameters of a probability distribution function?
Mean value μ and standard deviation σ
38What does standard deviation σ measure?
The spread or dispersion of the probability distribution
39What is the symbol for standard deviation?
σ
40What is variance?
The square of the standard deviation, σ²
41What is precision?
The degree of closeness or conformity of repeated measurements
42What is accuracy?
The degree of closeness or conformity of a measurement to the true value
43What is uncertainty?
The range within which the expected error of a measurement will fall