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LCCC Statistics
| Term | Definition |
|---|---|
| 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
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