Appendix F: Mathematical Phrases, Symbols, and Formulas
When the English says: Interpret this as: X is at least 4. X ≥ 4 The minimum of X is 4. X ≥ 4 X is no less than 4. X ≥ 4 X is greater than or equal to 4. X ≥ 4 X is at most 4. ...
| When the English says: | Interpret this as: |
| X is at least 4. | X ≥ 4 |
| The minimum of X is 4. | X ≥ 4 |
| X is no less than 4. | X ≥ 4 |
| X is greater than or equal to 4. | X ≥ 4 |
| X is at most 4. | X ≤ 4 |
| The maximum of X is 4. | X ≤ 4 |
| X is no more than 4. | X ≤ 4 |
| X is less than or equal to 4. | X ≤ 4 |
| X does not exceed 4. | X ≤ 4 |
| X is greater than 4. | X > 4 |
| X is more than 4. | X > 4 |
| X exceeds 4. | X > 4 |
| X is less than 4. | X < 4 |
| There are fewer X than 4. | X < 4 |
| X is 4. | X = 4 |
| X is equal to 4. | X = 4 |
| X is the same as 4. | X = 4 |
| X is not 4. | X ≠ 4 |
| X is not equal to 4. | X ≠ 4 |
| X is not the same as 4. | X ≠ 4 |
| X is different than 4. | X ≠ 4 |
Formula 1: Factorial n ! = n ( n − 1 ) ( n − 2 ) . . . ( 1 )
0
!
=
1
Formula 2: Combinations
(
n
r
)=
n!
(n−r)!r!
Formula 3: Binomial Distribution X~B(n,p)
P(X=x)=(
n
x
)
p
x
q
n−x
, for
x
=
0
,
1
,
2
,
.
.
.
,
n
Formula 4: Geometric Distribution X~G(p)
P(X=x)=
q
x−1
p
, for
x
=
1
,
2
,
3
,
.
.
.
Formula 5: Hypergeometric Distribution X~H(r,b,n)
P
(
X
=
x
)
=
(
(
r
x
)
(
b
n
−
x
)
(
r
+
b
n
)
)
Formula 6: Poisson Distribution X~P(μ)
P
(
X
=
x
)
=
μ
x
e
−
μ
x
!
Formula 7: Uniform Distribution X~U(a,b)
f(X)=
1
b−a
,
a
<
x
<
b
Formula 8: Exponential Distribution X~Exp(m)
f(x)=m
e
−mx
m>0,x≥0
Formula 9: Normal Distribution X~N(μ, σ 2 )
f
(
x
)
=
1
σ
2
π
e
−
(
x
−
μ
)
2
2
σ
2
,
–∞<x
<∞
Formula 10: Gamma Function Γ(z)= ∫ ∞ 0 x z−1 e −x dx z>0
Γ ( 1 2 ) = π
Γ ( m + 1 ) = m ! for m, a nonnegative integer
otherwise:
Γ(a+1)=aΓ(a)
Formula 11: Student's t-distribution X~ t df
f ( x ) = ( 1 + x 2 n ) − ( n + 1 ) 2 Γ ( n + 1 2 ) nπ Γ ( n 2 )
X = Z Y n
Z~N(0,1),Y~
Χ
df
2
, n = degrees of freedom
Formula 12: Chi-Square Distribution X~ Χ df 2
f
(
x
)
=
x
n
−
2
2
e
−
x
2
2
n
2
Γ
(
n
2
)
,
x>0 , n = positive integer and degrees of freedom
Formula 13: F Distribution X~F df(n),df(d)
df(n)= degrees of freedom for the numerator
df(d)= degrees of freedom for the denominator
f(x)= Γ( u+v 2 ) Γ( u 2 )Γ( v 2 ) ( u v ) u 2 x ( u 2 −1) [1+( u v ) x −0.5(u+v) ]
X = Y u W v , Y, W are chi-square
| Chapter (1st used) | Symbol | Spoken | Meaning |
| Sampling and Data | The square root of | same | |
| Sampling and Data | π | Pi | 3.14159… (a specific number) |
| Descriptive Statistics | Q1 | Quartile one | the first quartile |
| Descriptive Statistics | Q2 | Quartile two | the second quartile |
| Descriptive Statistics | Q3 | Quartile three | the third quartile |
| Descriptive Statistics | IQR | interquartile range | Q3 – Q1 = IQR |
| Descriptive Statistics | x ¯ | x-bar | sample mean |
| Descriptive Statistics | μ | mu | population mean |
| Descriptive Statistics | s sx sx | s | sample standard deviation |
| Descriptive Statistics | s2 sx2 | s squared | sample variance |
| Descriptive Statistics | σ σx σx | sigma | population standard deviation |
| Descriptive Statistics | σ2 σx2 | sigma squared | population variance |
| Descriptive Statistics | Σ | capital sigma | sum |
| Probability Topics | { } | brackets | set notation |
| Probability Topics | S | S | sample space |
| Probability Topics | A | Event A | event A |
| Probability Topics | P ( A ) | probability of A | probability of A occurring |
| Probability Topics | P(A|B) | probability of A given B | prob. of A occurring given B has occurred |
| Probability Topics | P(A OR B) | prob. of A or B | prob. of A or B or both occurring |
| Probability Topics | P(A AND B) | prob. of A and B | prob. of both A and B occurring (same time) |
| Probability Topics | A′ | A-prime, complement of A | complement of A, not A |
| Probability Topics | P(A') | prob. of complement of A | same |
| Probability Topics | G1 | green on first pick | same |
| Probability Topics | P(G1) | prob. of green on first pick | same |
| Discrete Random Variables | prob. distribution function | same | |
| Discrete Random Variables | X | X | the random variable X |
| Discrete Random Variables | X ~ | the distribution of X | same |
| Discrete Random Variables | B | binomial distribution | same |
| Discrete Random Variables | G | geometric distribution | same |
| Discrete Random Variables | H | hypergeometric dist. | same |
| Discrete Random Variables | P | Poisson dist. | same |
| Discrete Random Variables | λ | Lambda | average of Poisson distribution |
| Discrete Random Variables | ≥ | greater than or equal to | same |
| Discrete Random Variables | ≤ | less than or equal to | same |
| Discrete Random Variables | = | equal to | same |
| Discrete Random Variables | ≠ | not equal to | same |
| Continuous Random Variables | f(x) | f of x | function of x |
| Continuous Random Variables | prob. density function | same | |
| Continuous Random Variables | U | uniform distribution | same |
| Continuous Random Variables | Exp | exponential distribution | same |
| Continuous Random Variables | k | k | critical value |
| Continuous Random Variables | f(x) = | f of x equals | same |
| Continuous Random Variables | m | m | decay rate (for exp. dist.) |
| The Normal Distribution | N | normal distribution | same |
| The Normal Distribution | z | z-score | same |
| The Normal Distribution | Z | standard normal dist. | same |
| The Central Limit Theorem | CLT | Central Limit Theorem | same |
| The Central Limit Theorem | X ¯ | X-bar | the random variable X-bar |
| The Central Limit Theorem | μ x | mean of X | the average of X |
| The Central Limit Theorem | μ x ¯ | mean of X-bar | the average of X-bar |
| The Central Limit Theorem | σ x | standard deviation of X | same |
| The Central Limit Theorem | σ x ¯ | standard deviation of X-bar | same |
| The Central Limit Theorem | ΣX | sum of X | same |
| The Central Limit Theorem | Σx | sum of x | same |
| Confidence Intervals | CL | confidence level | same |
| Confidence Intervals | CI | confidence interval | same |
| Confidence Intervals | EBM | error bound for a mean | same |
| Confidence Intervals | EBP | error bound for a proportion | same |
| Confidence Intervals | t | Student's t-distribution | same |
| Confidence Intervals | df | degrees of freedom | same |
| Confidence Intervals | t α 2 | student t with a/2 area in right tail | same |
| Confidence Intervals | p′ ; p ^ | p-prime; p-hat | sample proportion of success |
| Confidence Intervals | q′ ; q ^ | q-prime; q-hat | sample proportion of failure |
| Hypothesis Testing | H 0 | H-naught, H-sub 0 | null hypothesis |
| Hypothesis Testing | H a | H-a, H-sub a | alternate hypothesis |
| Hypothesis Testing | H 1 | H-1, H-sub 1 | alternate hypothesis |
| Hypothesis Testing | α | alpha | probability of Type I error |
| Hypothesis Testing | β | beta | probability of Type II error |
| Hypothesis Testing | X1 ¯ − X2 ¯ | X1-bar minus X2-bar | difference in sample means |
| Hypothesis Testing | μ 1 − μ 2 | mu-1 minus mu-2 | difference in population means |
| Hypothesis Testing | P ′ 1 − P ′ 2 | P1-prime minus P2-prime | difference in sample proportions |
| Hypothesis Testing | p 1 − p 2 | p1 minus p2 | difference in population proportions |
| Chi-Square Distribution | Χ 2 | Ky-square | Chi-square |
| Chi-Square Distribution | O | Observed | Observed frequency |
| Chi-Square Distribution | E | Expected | Expected frequency |
| Linear Regression and Correlation | y = a + bx | y equals a plus b-x | equation of a line |
| Linear Regression and Correlation | y^ | y-hat | estimated value of y |
| Linear Regression and Correlation | r | correlation coefficient | same |
| Linear Regression and Correlation | ε | error | same |
| Linear Regression and Correlation | SSE | Sum of Squared Errors | same |
| Linear Regression and Correlation | 1.9s | 1.9 times s | cut-off value for outliers |
| F-Distribution and ANOVA | F | F-ratio | F-ratio |
