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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


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 ~ E x p ( m )

f ( x ) = m e m x 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 d x z > 0

Γ ( 1 2 ) = π

Γ ( m + 1 ) = m ! for m , a nonnegative integer

otherwise: Γ ( a + 1 ) = a Γ ( a )

Formula 11: student's t -distribution

X ~ t d f

f ( x ) = ( 1 + x 2 n ) ( n + 1 ) 2 Γ ( n + 1 2 ) Γ ( n 2 )

X = Z Y n

Z ~ N ( 0 , 1 ), Y ~ Χ d f 2 , n = degrees of freedom

Formula 12: chi-square distribution

X ~ Χ d f 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 d f ( n ) , d f ( d )

d f ( n ) = degrees of freedom for the numerator

d f ( 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

Symbols and their meanings

Symbols and their meanings
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 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 ¯ x-bar sample mean
Descriptive Statistics μ mu population mean
Descriptive Statistics s s x sx s sample standard deviation
Descriptive Statistics s 2 s x 2 s squared sample variance
Descriptive Statistics σ σ x σx sigma population standard deviation
Descriptive Statistics σ 2 σ x 2 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 G 1 green on first pick same
Probability Topics P ( G 1 ) prob. of green on first pick same
Discrete Random Variables PDF 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 pdf 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 Σ X sum of X same
The Central Limit Theorem Σ x 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 X 1 ¯ X 2 ¯ X 1-bar minus X 2-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 P 1-prime minus P 2-prime difference in sample proportions
Hypothesis Testing p 1 p 2 p 1 minus p 2 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 1.9 s 1.9 times s cut-off value for outliers
F -Distribution and ANOVA F F -ratio F -ratio

Questions & Answers

discuss the roles of vital and health statistic in the planning of health service of the community
given that the probability of
can man city win Liverpool ?
Emmanuel Reply
There are two coins on a table. When both are flipped, one coin land on heads eith probability 0.5 while the other lands on head with probability 0.6. A coin is randomly selected from the table and flipped. (a) what is probability it lands on heads? (b) given that it lands on tail, what is the Condi
Nusrat Reply
what is gradient descent?
Saurav Reply
It should be a Machine learning terms。
it is a term used in linear regression
what are the differences between standard deviation and variancs?
what is statistics
Emmanuel Reply
statistics is the collection and interpretation of data
the science of summarization and description of numerical facts
Is the estimation of probability
mr. zaini..can u tell me more clearly how to calculated pair t test
do you have MG Akarwal Statistics' book Zaini?
Haai how r u?
maybe .... mathematics is the science of simplification and statistics is the interpretation of such values and its implications.
can we discuss about pair test
what is outlier?
Usama Reply
outlier is an observation point that is distant from other observations.
what is its effect on mode?
Outlier  have little effect on the mode of a given set of data.
How can you identify a possible outlier(s) in a data set.
The best visualisation method to identify the outlier is box and wisker method or boxplot diagram. The points which are located outside the max edge of wisker(both side) are considered as outlier.
@Daniel Adunkwah - Usually you can identify an outlier visually. They lie outside the observed pattern of the other data points, thus they're called outliers.
what is completeness?
I am new to this. I am trying to learn.
I am also new Dom, welcome!
please my friend i want same general points about statistics. say same thing
outliers do not have effect on mode
also new
I don't get the example
Hadekunle Reply
ways of collecting data at least 10 and explain
Ridwan Reply
Example of discrete variable
Bada Reply
sales made monthly.
I am new here, can I get someone to guide up?
dies outcome is 1, 2, 3, 4, 5, 6 nothing come outside of it. it is an example of discrete variable
continue variable is any value value between 0 to 1 it could be 4digit values eg 0.1, 0.21, 0.13, 0.623, 0.32
How to answer quantitative data
Alhassan Reply
what's up here ... am new here
sorry question a bit unclear...do you mean how do you analyze quantitative data? If yes, it depends on the specific question(s) you set in the beginning as well as on the data you collected. So the method of data analysis will be dependent on the data collecter and questions asked.
how to solve for degree of freedom
Quantitative data is the data in numeric form. For eg: Income of persons asked is 10,000. This data is quantitative data on the other hand data collected for either make or female is qualitative data.
Degree of freedom is the unconditionality. For example if you have total number of observations n, and you have to calculate variance, obviously you will need mean for that. Here mean is a condition, without which you cannot calculate variance. Therefore degree of freedom for variance will be n-1.
data that is best presented in categories like haircolor, food taste (good, bad, fair, terrible) constitutes qualitative data
vegetation types (grasslands, forests etc) qualitative data
I don't understand how you solved it can you teach me
Caleb Reply
solve what?
What is the end points of a confidence interval called?
lower and upper endpoints
Class members write down the average time (in hours, to the nearest half-hour) they sleep per night.
William Reply
how we make a classes of this(170.3,173.9,171.3,182.3,177.3,178.3,174.175.3)
why is always lower class bundry used
Assume you are in a class where quizzes are 20% of your grade, homework is 20%, exam _1 is 15%,exam _2 is 15%, and the final exam is 20%.Suppose you are in the fifth week and you just found out that you scored a 58/63 on the fist exam. You also know that you received 6/9,8/10,9/9 on the first
Diamatu Reply
quizzes as well as a 9/11,10/10,and 4.5/7 on the first three homework assignment. what is your current grade in the course?
the answer is 2.6
if putting y=3x examine that correlation coefficient between x and y=3x is 1.
Aadrsh Reply

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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