Mathematical Phrases, Symbols, and Formulas
English Phrases Written Mathematically
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 |
Formulas
Formula 1: Factorial
Formula 2: Combinations
Formula 3: Binomial Distribution
, for
Formula 4: Geometric Distribution
, for
Formula 5: Hypergeometric Distribution
Formula 6: Poisson Distribution
Formula 7: Uniform Distribution
,
Formula 8: Exponential Distribution
Formula 9: Normal Distribution
,
Formula 10: Gamma Function
for , a nonnegative integer
otherwise:
Formula 11: Student’s t-distribution
, = degrees of freedom
Formula 12: Chi-Square Distribution
, , = positive integer and degrees of freedom
Formula 13: F Distribution
degrees of freedom for the numerator
degrees of freedom for the denominator
, , are chi-square
Symbols and Their Meanings
Chapter (1st used) | Symbol | Spoken | Meaning |
---|---|---|---|
Sampling and Data | The square root of | same | |
Sampling and Data | Pi | 3.14159… (a specific number) | |
Descriptive Statistics | Q_{1} | Quartile one | the first quartile |
Descriptive Statistics | Q_{2} | Quartile two | the second quartile |
Descriptive Statistics | Q_{3} | Quartile three | the third quartile |
Descriptive Statistics | IQR | interquartile range | Q_{3} – Q_{1} = IQR |
Descriptive Statistics | x-bar | sample mean | |
Descriptive Statistics | mu | population mean | |
Descriptive Statistics | ss_{x}sx | s | sample standard deviation |
Descriptive Statistics | s squared | sample variance | |
Descriptive Statistics | σx | sigma | population standard deviation |
Descriptive Statistics | sigma squared | population variance | |
Descriptive Statistics | capital sigma | sum | |
Probability Topics | brackets | set notation | |
Probability Topics | S | sample space | |
Probability Topics | Event A | event A | |
Probability Topics | probability of A | probability of A occurring | |
Probability Topics | probability of A given B | prob. of A occurring given B has occurred | |
Probability Topics | prob. of A or B | prob. of A or B or both occurring | |
Probability Topics | 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 | G_{1} | green on first pick | same |
Probability Topics | P(G_{1}) | 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 | 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-bar | the random variable X-bar | |
The Central Limit Theorem | mean of X | the average of X | |
The Central Limit Theorem | mean of X-bar | the average of X-bar | |
The Central Limit Theorem | standard deviation of X | same | |
The Central Limit Theorem | standard deviation of X-bar | same | |
The Central Limit Theorem | sum of X | same | |
The Central Limit Theorem | 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 | student t with a/2 area in right tail | same | |
Confidence Intervals | ; | p-prime; p-hat | sample proportion of success |
Confidence Intervals | ; | q-prime; q-hat | sample proportion of failure |
Hypothesis Testing | H-naught, H-sub 0 | null hypothesis | |
Hypothesis Testing | H-a, H-sub a | alternate hypothesis | |
Hypothesis Testing | H-1, H-sub 1 | alternate hypothesis | |
Hypothesis Testing | alpha | probability of Type I error | |
Hypothesis Testing | beta | probability of Type II error | |
Hypothesis Testing | X1-bar minus X2-bar | difference in sample means | |
Hypothesis Testing | mu-1 minus mu-2 | difference in population means | |
Hypothesis Testing | P1-prime minus P2-prime | difference in sample proportions | |
Hypothesis Testing | p1 minus p2 | difference in population proportions | |
Chi-Square Distribution | Ky-square | Chi-square | |
Chi-Square Distribution | Observed | Observed frequency | |
Chi-Square Distribution | 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-hat | estimated value of y | |
Linear Regression and Correlation | correlation coefficient | same | |
Linear Regression and Correlation | 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 |