[PDF] [PDF] Statistics - Cheat-Sheetsorg

[PDF] Statistics Cheat Sheet - MIT

Statistics Cheat Sheet Population The entire group can be taken from a population Reflects the extent to which a statistic changes from sample to sample

[PDF] Stat 100 Final Cheat Sheets - Google Docs - Fas Harvard

P(at least 1 failure) = 1 pn 5 ) Binomial Distribution Formula for x=exact value 6 ) Mean (Expectation) (x) p μ = E = n 7 ) Variance and Standard Dev pq σ2 = n

[PDF] Frequently Used Statistics Formulas and Tables

Sample Size for Estimating variance or standard deviation: *see table 7-2 (last page of formula sheet) Confidence Intervals Level of Confidence z-value ( /2 z α )

[PDF] TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics

same formula after adding 2 successes and two failures to the data • z test statistic for H0 : p = p0 (large SRS): z = ˆp − p0 √p0(1 − p0) n P-values from N( 0,1)

[PDF] Statistics - Cheat-Sheetsorg

I Descriptive Statistics - procedures used to organize and of sample data according to certain specified The formula is n less number of restrictions In this

[PDF] A Statistics Summary-sheet

A Statistics Summary-sheet Sampling Conditions Confidence Interval Test Statistic σ 2 is known ⇒ X Formulas, Distributions, and Concepts Counting and 

[PDF] Statistics Formula Sheet and Tables 2020 - AP Central

critical value standard error of statistic ± Chi-square statistic: ( ) 2 observed expected expected χ − = ∑ 2 AP Statistics 2020 Formulas and Tables Sheet 

[PDF] AP Statistics Formula Sheet

AP Statistics Formula Sheet (I) Descriptive Statistics 2 2 1 1 2 1 1 2 Confidence interval: statistic ± (critical value) • (standard deviation of statistic) Single– 

[PDF] Important Concepts not on the AP Statistics Formula Sheet

Important Concepts not on the AP Statistics Formula Sheet Part I: IQR = Q3 – Q1 Test for an outlier: 1 5(IQR) above Q3 or below Q1 The calculator will run the

[PDF] Formula Sheet for Final Exam

Formula Sheet for Final Exam Summary Statistics • Sample mean: ¯x = n ∑ i=1 xi n Test statistic for difference of two sample means, H0 : µ1 − µ2 = d0,

[PDF] statistics formulas class 12

[PDF] statistics lecture notes pdf

[PDF] statistics of paramagnetism

[PDF] statistics on flexible working

[PDF] statistics using excel tutorial

[PDF] statistique exercices corrigés

[PDF] stats that prove lebron is the goat

[PDF] status of sewage treatment in india

[PDF] status signal in 8086

[PDF] statutory holidays 2020 usa

[PDF] stay in place bridge deck forms

[PDF] stayman convention audrey grant

[PDF] std 9 maths chapter 2

[PDF] steady state exercise physiology

[PDF] steel deck institute

.TLI\

TSTICS FOR INTRODUGTORY COURSES

J STATISTICS - A set of tools for collecting,

oreanizing, presenting, and analyzing numerical facts or observations.

I . Descriptive Statistics - procedures used to

organize and present data in a convenient, useable. and communicable form.

2. Inferential Statistics - procedures employed

to arrive at broader generalizations or inferences from sample data to populations. -l STATISTIC - A number describing a sample characteristic. Results from the manipulation of sample data according to certain specified procedures.

J DATA - Characteristics or numbers that

are collected by observation.

J POPULATION - A complete set of actual

or potential observations.

J PARAMETER - A number describing a

population characteristic; typically, inferred from sample statistic. f SAMPLE - A subset of the population selected according to some scheme.

J RANDOM SAMPLE - A subset selected

in such a way that each member of the population has an equal opportunity to be selected. Ex.lottery numbers in afair lottery

J VARIABLE - A phenomenon that may take

on different values. f MEAN -The ooint in a distribution of measurements about which the summed deviations are equal to zero.

Average value of a sample or population.

POPULATION MEAN SAMPLE MEAN

p: +!,*,o:#2*, Note: The mean ls very sensltlve to extreme measure- ments that are not balanced on both sides.

I WEIGHTED MEAN - Sum of a set of observations

multiplied by their respective weights, divided by the sum of the weights: 9, *, *,

WEIGHTED MEAN -L-

,\r*'where xr, : weight,'x, - observation; G : number of observaiion grdups.'Calculated from a population. sample. or gr6upings in a frequency distribution. Ex. In the FrequencVDistribution below, the meun is

80.3: culculatbd by- using frequencies for the wis.

When grouped, use closs midpoints Jbr xis.

J MEDIAN - Observation or potenlial observation in a set that divides the set so that the same number of observations lie on each side of it. For an odd number of values. it is the middle value; for an even number it is the average of the middle two. Ex. In the Frequency Distribution table below, the median is 79.5. f MODE - Observation that occurs with the greatest tiequency. Ex. In the Frequency Distributioln nble below. the mode is 88.

O SUM OF SOUARES fSSr- Der iations tiom

the mean. squared and summed: , (I r,),PopulationSS:I(Xi -l.rx)'or Ixi'- t N _ r, \,)2Sample SS:I(xi -x)2or Ixi2---

O VARIANCE - The average of square differ-

ences between observations and their mean.

POPULANONVARIANCE SAMPLEVARIANCE

VARIANCES FOH GBOUPED DATA

POPUIATION SAMPLE

^{G-'{Go2:*i t,(r,-p )t s2=;1i tilm'-x;2 lI ;_r t=1

D STANDARD DEVIATION - Square root of

the variance:

Ex. Pop. S.D. o -

nY IUfiz

D BAR GRAPH - A form of graph that uses

bars to indicate the frequency of occurrence of observations. o Histogram - a form of bar graph used rr ith interval or ratio-scaled variables. - Interval Scale- a quantitative scale that permits the use of arithmetic operations. The zero point in the scale is arbitrary. - R.atio Scale- same as interval scale excepl that there is a true zero point.

D FREOUENCY CURVE - A form of graph

representing a frequency distribution in the form of a continuous line that traces a histogram. o Cumulative Frequency Curve - a continuous line that traces a histogram where bars in all the lower classes are stacked up in the adjacent higher class. It cannot have a negative slop€. o Normal curve - bell-shaped curve. o Skewed curve - departs from symmetry and tails-off at one end.

GROUpITGOF DATA

Shows the number of times each observation

occurs when the values ofa variable are arranged in order according to their magnitudes.

II GROTJPED FREOUENCY EilSTRIBUTION

- A frequency distribution in which the values ofthe variable have been grouped into classes.

J il {il, I a rr I.)'A .l b]|, K I 3artl LQ

xfxtxfxt

100183117411f65o

991ut11111751111661

98085176116711

gl086o77111681

96118717AI69111

9508811111117911701111

94089111801710

93I1181117211

92091182I73111

tr CUMULATUE FREOUENCY BISTRI.

BUTION -A distribution which shows the to-

tal frequency through the upper real limit of each class. tr CUMUIATIVE PERCENTAGE DISTRI.

BUTION-A distribution which shows the to-

tal percentage through the upper real limit of each class. !I!llrfGl:I il {.lllNl.l'tlz CLASS f

ICum f"

65-67334.84

6&7081117.74

71-7351625.81

7+7692540.32

Tt-7963150.00

80-8243556.45

83-8584369.35

86-8885182.26

89-9165791.94

92-g15893.55

95-9726096.77

9&100262100.00

15 10 0

NORMAL CURVE

^/T\./\ -t -att?\CLASS f CLASS t

98-100

15 10 0

SKEWED CURVE

--\/\-/LEFT\ J-\ Probability of occurrence^t at -Number of outcomafamring EwntA oif'ent'l Ant=@

D SAMPLE SPACE - All possible outcomes of an

experiment.

N TYPE OF EVENTS

o Exhaustive - two or more events are said to be exhaustive if all possible outcomes are considered.

Symbolically, P (A or B or...) - l.

rNon-Exhausdve -two or more events are said to be non- exhaustive if they do not exhaust all possible outcomes. rMutually Exclusive - Events that cannot occur simultaneously:p (A and B) = 0; and p (A or B) = p (A) + p (B).

Ex. males, females

oNon-Mutually Exclusive - Event-s that can occur simultaneously: p (A orB) = P(A) +p(B) - p(A and B)' &x. males, brown eyes. Slndependent - Events whose probability is unaffected by occurrence or nonoccurrence of each other: p(A lB) = p(A); ptB In)= p(e); and p(A and B) = p(A) p(B).

Ex. gender and eye color

SDependent - Events whose probability changes

deoendlns upon the occurrence or non-occurrence ofeach other: p{.I I bl dilfers lrom AA): p(B lA) differs from p(B); and p(A and B): p(A) p(BlA): p(B) AAIB)

Ex. rsce and eye colon

C JOINT PROBABILITIES - Probability that2 ot

more events occur simultaneously. tr MARGINAL PROBABILITIES or Uncondi- tional Probabilities = summation of probabilities'

D CONDITIONAL PROBABILITIES - Probability

of I given the existence of ,S, written, p (Al$. fl EXAMPLE- Given the numbers I to 9 as observations in a sample space: .Events mutually exclusive and exhaustive'

Example: p (all odd numb ers) ; p ( all eu-e n nurnbers ).Evenls mutualty exclusive but not exhaustive-

Example: p (an eien number); p (the numbers 7 and 5) .Events ni:ither mutually exclusive or exhaustive-

Example: p (an even number or a 2)

fl SAMPLING DISTRIBUTION - A theoretical probability distribution of a statistic that would iesult from drawing all possible samples of a given size from some population.

THE STAIUDARD EBROROF THE MEAN

A theoretical standard deviation of sample mean of a given sample si4e, drawn from some speciJied popu- lation. DWhen based on a very large, known population, the standard error is: 6_ _ o"r_ ^l n EWhen estimated from a sample drawn from very large population, the standard error is: lThe dispersion of sample means decreases as sample size is increased. O== S ^t-'fn

RANDOM VARIABLES

A mapping or function that assigns one and'onlv one-numerical value to each outcome in an exPeriment. tl DISCRETE RANDOM VARIABLES - In- volves rules or probability models for assign- ing or generating only distinct values (not frac- tional measurements).

C BINOMIAL DISTRIBUTION - A model

for the sum of a series of n independent trials where trial results in a 0 (failure) or I (suc- cess). Ex. Coin to"t p(r) =(!)n'l-trl"-' where p(s) is the probability of s success in n trials with a constant n probability per trials, and where (,1\= , n!-"- "'-'- ts/ s!(n-s)!

Binomial mean: !: nx

Binomial variance: o': n, (l - tr)

As n increases, the Binomial approaches the

Normal distribution.

D HYPERGEOMETRIC DISTRIBUTION -

A model for the sum of a series of n trials where

each trial results in a 0 or I and is drawn from a small population with N elements split between

N1 successes and N2 failures. Then the probabil-

ity of splitting the n trials between xl successes and x2 failures is: Nl! {_z! p(xlandtrr:W 't 4tlv-r;lr Hypergeometric mean : pt :E(xi - +and variance: o2 : ffit+][p]

D POISSON DISTRIBUTION - A model for

the number of occurrences of an event x :

0,1,2,..., when the probability of occurrence

is small, but the number of opportunities for the occurrence is large, for x : 0,1,2,3.... and )v > 0 . otherwise P(x) =. 0. e$t=ff

Poisson mean and rariance: ,t.

Fo r c ontinuo u s t' a ri u b I e s. .fi'e q u e n t' i e s u re e.t p re s s e d in terms o.f areus under u t'ttt.re.

D CONTINUOUS RANDOM VARIABLES

- Variable that may take on any value along an uninterrupted interval of a numberline.

D NORMAL DISTRIBUTION - bell cun'e;

a distribution whose values cluster symmetri-quotesdbs_dbs12.pdfusesText_18