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LCCC Statistics

Statistics The science or study of data
Data Info gained from counting, measurements, surveys/response, or experiments
Population everyone or everything you wish to study
Census a study of the entire population
Sample a part, portion, or subset of population
Parameter any number that describes a population
N population size ( number of data in a population)
Statistic any number that describes a sample
n sample size ( number of data in sample)
Descriptive Statistics organizing, displaying, and analyzing (calculations)
Inferential Statistics make a decision/conclusion based on a sample
Qualitative data describes, labels, categories, ranking
Nominal No meaningful order to categories
Ordinal meaningful order to categories
Quantitative data numerical data (except description)
Discrete any countable data
Continuous any form of measurement, any value on the number line, interval data
Interval level of measurement meaningful differences between values, 0 is a placeholder
Ratio level of measurement meaningful ratio/ ("twice as many"), 0 is nothing or none
Statistical Study Goal make a decision about the population based on a sample
Steps to Design a Study 1) decide the population 2) best method for data collection 3) Collect Data 4) Summarize and analyze data 5) Make a conclusion 6) Consider any possible errors
Observational Study watch and record, do not interact/implement change
Perform an experiment part of the sample is changed and then you compare
Simulation a physical/ computer imitation of real life
Survey interview and record responses ( in person, mail, paper, telephone, email)
Center value that indicates where the MIDDLE of data set is
Variation a measure of the amount the data values VARY
Distribution shape/spread of data over a range
Frequency Distribution Table table that lists all categories/ classes/ intervals and the COUNT of data values in each class
Class interval used to split up/organize data values into a frequency distribution
frequency of class number of data values in that class
n=sample size total number of data values in study
range highest data value - lowest data value
lower class limit smallest possible number that belongs to each class
upper class limit largest possible number that belongs to each class
class width difference between 2 consecutive lower class limits
Frequency Histogram touching bar graph, x=class midpoints, y=frequency
Frequency Polygon line graph that represents continuous change, x=class midpoints, y=frequency, need a midpoint less and higher than table midpoints for frequency of 0
Relative Frequency Histogram touching bar graph, x= class midpoints, y= relative frequency
Ogive line graph with no closure, x= class boundaries, y= cumulative frequency
Class Midpoint (lower class limit + its upper class limit)/2
relative frequency (class frequency/ total frequency)x100%
cumulative frequency class frequency + all previous frequencies
class boundary the average between a upper limit and the next lower limit
Dot Plot each data value represented as a point (dot) above a horizontal axis, multiple data values are represented by stacked dots
Pareto Chart bar graph ( not touching) with decreasing frequencies from left to right
Range R=max value - mininum value
Deviation difference of value and mean of data set ( dev= x- mean)
Variance average of the squared deviations from the mean ( take each deviation and square it)
Standard Deviation square root of the variance ((E(x-m)^2)/N) sample=same but n-1
Empirical Rule 68% of data= 1 stdev., 95% of data= 2 stdev, 99.7% of data= 3 stdev
Empirical Rule Unusual more than 2 standard deviations away from the mean ( outlier??)
Empirical Rule Very Unusual more than 3 standard deviations away from the mean (outlier***)
First Quartile (Q1) 25% of the data is at or below ( median of lower half)
Second Quartile (Q2) 50% of the data is at or below (median)
Third Quartile (Q3) 75% of the data is at or below ( median of lower half)
Interquartile Range (IQR) Q3-Q1
Finding Outlier fences step= IGR(1.5), Q1- step, Q3 + step
Five number summary min, Q1, Q2, Q3, max
Percentile breaks a data set up into 100 equal parts (Pk=Kth percentile)
Standard Score (z-score) z=(x-mean/st.dev.)
Quartile splits the data into 4 equal parts
probability experiment action/trial through which specific results are obtained
outcome result of a single trial
sample space (S) set of all possible outcomes
event(E) subset(part) of a sample space
simple event event with single outcome
compound event more than one outcome
fundamental counting principle if one event can occur in "m" ways and a second event can occur in "n" ways, the # of ways both events occur in sequence is:
subjective probability result from intuition, educated guess, estimates
empirical/statistical probability based on observations P(E)=freq. of E./total freq.
classical/theoretical probability # of outcome in E(# favorable)/total # of possible outcomes(# in S)
law of large numbers as an experiment is repeated over and over, empirical probability of an event approaches the theoretical(actual) probability of the event
properties of probability 1) 0<=P(E)<=1 prob. is never negative prob. is never bigger than 1 2)P(E)=1=certain event 3)P(E)=0=impossible event EP(S)=1
complement of event E P(not E)=P(E^1) P(not E)=1-P(E)
conditional probability probability of B given that A has already occurred P(B|A)=P(B and A)/P(A)
independent events one event does NOT affect the probability of the occurrence of the other event P(B|A)=P(B)
dependent events the first affects the second conditional
multiplication rule probability that 2 events occur in sequence P(A and B)=P(A and then B) independent=P(A and B)=P(A)*P(B) dependent=P(A and B)=P(A)*P(B|A)
mutually exclusive A and B can't occur at the same time
addition rule not mutually exclusive=P(A)+P(B)-P(A and B) mutually exclusive=P(A)+P(B)
n factorial n!=n(n-1)(n-2)...3*2*1 3!=3*2*1=6
permutation an arrangement of "n" objects, taking "n" objects and putting them in order n!
permutations of n objects taken r at a time "n" objects=group of "r" objects, order matters!!! nPr=n!/(n-r)!
distinguishable permutations ordered arrangement, repeats!, n!/(n1!n2!...nk!)
Combinations a part of the whole group, order does not matter, nCr=n!/(r!(n-r)!)
Created by: 14diltzd