1The closeness of a measurement to the true value
Accuracy
2The closeness of repeated measurements to one another
Precision
3The degree of doubt associated with a measurement or its estimated range
Uncertainty
4A measure of the spread or variation of observations
Standard deviation
5The square of the standard deviation
Variance
6A measurement error caused by natural or physical conditions
Natural/Physical error
7A measurement error caused by imperfections or limitations of an instrument
Instrumental error
8A measurement error caused by the observer or surveyor
Personal error
9An error caused by mistakes, blunders, or carelessness
Gross error
10An error that follows a consistent pattern or bias
Systematic error
11An error that remains after gross and systematic errors have been removed
Random error
12The difference between the measured value and the true value
Error
13The difference between an estimated value and an observed value
Residual
14The formula for error between a measured value and the true value
ε = χ − τ
15The formula for residual
v = χ̂ − χ
16The arithmetic average of a set of observations
Mean
17The number of times an observation or value occurs
Frequency
18The ratio of a frequency to the total number of observations
Relative frequency
19The limiting value of relative frequency as the number of observations becomes very large
Probability
20The probability of an event not occurring
Complement
21The probability that two independent events both occur
Intersection
22Two events that cannot occur at the same time
Mutually exclusive events
23Two events whose occurrence does not affect each other
Independent events
24A variable whose possible values are numerical outcomes of a random process
Random variable
25A random variable that takes countable or distinct values
Discrete random variable
26A random variable that can take any value within an interval
Continuous random variable
27A function that describes the probability density of a continuous random variable
Probability density function (PDF)
28The probability represented by the area under a PDF between two values
Interval probability
29The function giving the probability that a random variable is less than or equal to a value
Cumulative distribution function (CDF)
30The probability that a continuous random variable takes one exact value
0
31The distribution characterized by a bell-shaped curve
Normal distribution
32The standardized value indicating how many standard deviations an observation is from the mean
Z-score
33The formula for a Z-score
Z = (X − μ) / σ
34The formula for finding X from a Z-score
X = μ + Zσ
35A value above the mean in a normal distribution has this type of Z-score
Positive Z-score
36A value below the mean in a normal distribution has this type of Z-score
Negative Z-score
37The percentage within ±1 standard deviation of the mean in a normal distribution
68.3%
38The percentage within ±2 standard deviations of the mean in a normal distribution
95.4%
39The percentage within ±3 standard deviations of the mean in a normal distribution
99.7%
40The percentage within ±1.960 standard deviations of the mean
95%
41The percentage within ±2.576 standard deviations of the mean
99%
42A method used to approximate a nonlinear function using a linear relationship around a known point
Linearization
43The first-order approximation of a function using its derivative
First-order Taylor approximation
44The value of a function at the initial or known values
y₀
45The matrix containing the partial derivatives used in linearization
Jacobian
46The change in the input variables used in linearization
Δx
47The general first-order linearization relationship
y = y₀ + JΔx
48The method of determining how errors in input measurements affect the output quantity
Error propagation
49The differential form used to express first-order error propagation
dy = JΔx
50The derivative of a function with respect to one variable while treating other variables as constant
Partial derivative
51The total differential used to approximate the change in a function
Total differential
52For A = x₁x₂, the differential representing the propagated change in area
dA = x₂dx₁ + x₁dx₂
53The variation of one variable with itself
Variance
54A measure of how two variables change together
Covariance
55Positive covariance indicates that two variables tend to change in this direction
Same direction
56Negative covariance indicates that two variables tend to change in this direction
Opposite directions
57Covariance close to zero generally indicates this type of relationship
Little or no linear relationship
58The sample covariance formula
Cov(X,Y) = Σ[(Xi − X̄)(Yi − Ȳ)] / (n − 1)
59The population covariance formula
Cov(X,Y) = Σ[(Xi − μX)(Yi − μY)] / n
60The relationship between variance and covariance
Var(X) = Cov(X,X)
61The population standard deviation formula
σ = √[Σ(xi − μ)² / n]
62The sample standard deviation formula
s = √[Σ(xi − x̄)² / (n − 1)]
63The population variance formula
σ² = Σ(xi − μ)² / n
64The sample variance formula
s² = Σ(xi − x̄)² / (n − 1)
65The number of observations in a population or dataset
n
66The value representing the population mean
μ
67The value representing the sample mean
x̄
68The population standard deviation symbol
σ
69The sample standard deviation symbol
s
70A smaller standard deviation generally indicates this
Greater precision
71The process of modifying observations so they satisfy required mathematical or geometric conditions
Adjustment
72The minimum number of observations required to determine the unknowns
Minimum number of measurements
73The number of observations beyond the minimum required
Redundancy
74The difference added to an observation during adjustment
Correction
75The adjusted or estimated value of an observation
Adjusted observation
76The method that determines the most likely values by minimizing the sum of squared residuals
Least squares
77The quantity minimized in the least-squares method
Σv²
78An observation that is estimated after adjustment
L̂ or adjusted observation
79The condition that measurements must satisfy after adjustment
Condition equation
80A system containing equations that relate observations and unknown quantities
Linear system
81A rectangular arrangement of numbers or mathematical quantities
Matrix
82The number of rows and columns defining a matrix's size
Dimension
83A matrix with the same number of rows and columns
Square matrix
84A square matrix whose determinant is zero
Singular matrix
85A square matrix whose determinant is nonzero
Nonsingular matrix
86The numerical value associated with a square matrix used to determine properties such as invertibility
Determinant
87A matrix that satisfies AA⁻¹ = I
Inverse matrix
88A matrix with ones on the main diagonal and zeros elsewhere
Identity matrix
89The operation that changes rows into columns
Transpose
90The matrix obtained by interchanging rows and columns
Transpose matrix
91A numerical value multiplied by a matrix
Scalar
92The operation of multiplying corresponding matrices according to matrix multiplication rules
Matrix multiplication
93A system of equations involving unknown variables
System of linear equations
94A numerical method that eliminates variables using row operations
Gaussian elimination
95A numerical method that reduces an augmented matrix to reduced row-echelon form
Gauss-Jordan elimination
96A numerical method that repeatedly improves an initial estimate using equations solved for each variable
Jacobi method
97A numerical method similar to Jacobi but immediately uses newly calculated values
Gauss-Seidel method
98A decomposition expressing a matrix as the product of a lower and upper triangular matrix
LU decomposition
99The lower triangular matrix in LU decomposition
L
100The upper triangular matrix in LU decomposition
U
101The equation solved first in LU decomposition
LY = B
102The equation solved second in LU decomposition
UX = Y
103A measure describing how close measurements are to each other
Precision
104A measure describing how close measurements are to the accepted or true value
Accuracy
105A range or indication describing possible variation in a measured quantity
Uncertainty