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Quant. Exam
N/A
37
Mathematics
10/23/2012

Term
 Statistics
Definition
 the science of collecting, classifying, summarizing, organizing and interpreting data
Term
 Experimental Unit
Definition
 the object upon which we collect data. It is the source of each “observation”.   In our water research, it is a bit of water taken from a segment of the brook at a particular time.
Term
 Variable
Definition
 a characteristic of the experimental unit that is measured from one observation to the next. In our water research, it could be concentration of nitrate
Term
 Population
Definition
 a collection of data on all experimental units. The population is all possible observations.
Term
 Sample
Definition
 a subset of the population
Term
 Descriptive statistics
Definition
 summarize the sample data
Term
 Inferential statistics
Definition
 use the sample data to say something about the population give a measure of reliability (i.e. precision, confidence) about the population parameters
Term
 Sampling Frame
Definition
 a list of all units in the population.
Term
 Simple Random Sample
Definition
 every unit in the population has the same probability of being selected for the sample and the probabilities are independent
Term
 Stratified Random Sampling
Definition
 the population units are partitioned into strata, then simple random sampling is carried out in each stratum
Term
 Clustered Sampling
Definition
 units are selected according to clusters
Term
 Systematic Sampling
Definition
 every Kth element is selected
Term
 Sampling “Bias”
Definition
 exists when some subset of the population has uneven and unaccounted for probability of selection Non-response in surveys can be a type of bias
Term
 “Measurement error”
Definition
 is the difference between the actual value of the variable and the recorded value of the variable. Measurement error can be a type of bias. A faulty thermometer can produce measurement error
Term
 “Sampling error”
Definition
 refers to the natural variation in any simple random sample. Not mistake.   1.Bias + Sampling Error = the difference between reality and your observations = TOTAL ERROR
Term
 Central Tendency
Definition
 –Mean is the average   –Median is the middle observation of ordered data   •Definition is slightly different for Odd n versus Even n   Mode is the value that occurs with the greatest frequency
Term
 •Variation
Definition
 –Range = Maximum minus Minimum   –Variance   –Standard Deviation is square root of variance   •When the distribution is bell shaped: –about 70% of observations are within one standard deviation of the mean –about 95% of observations are within two standard deviations of the mean –Inter-quartile range = 3rd Quartile minus 1st Quartile
Term
 Pth Percentile
Definition
 the value at which P% of the observations fall on or below and (100-P)% of the observations fall above   •Max is 100th percentile   •Third quartile is 75th percentile   •mid-quartile is 50th percentile, which is the median     •First quartile is 25th percentile     •Min is 0th percentile
Term
 Z-score
Definition
 Z-score = ( Xi – Xbar ) / s, where s is the standard deviation
Term
 Outliers
Definition
 •Candidates for outliers have z-scores less than –3 or greater than +3
Term
 Skewness
Definition
 If the distribution is symmetric, then it is not skewed If the tail of the distribution extends to the right, then the distribution is skewed right, i.e. skewed in the positive direction If the tail of the distribution extends to the left, then the distribution is skewed left, i.e. skewed in the negative direction
Term
 •Notation for population parameters and sample statistics on page 179
Definition
 –Mean •Mu is parameter, Xbar is statistic –Variance •sigma2 is parameter, s2 is statistic –Standard Deviation •sigma is parameter, s is statistic –Z-score •z is parameter, z is statistic –Correlation coefficient •rho is parameter, r is statistic
Term
 Range
Definition
 –Maximum minus Minimum
Term
 Frequentist view of probability
Definition
 –Probability is the number of times that an event happens divided by the number of trials
Term
 Bayesian view of probability
Definition
 Probability is a person’s subjective judgment concerning the likelihood of an event, based on the information that the person has
Term
 Experiment
Definition
 is the process of making observation(s) on unit(s)   –Selecting a card from a deck –Flipping a thumbtack –Observing the cloudiness of the sky
Term
 Event
Definition
 the outcome of an experiment   –The card is red –The thumbtack lands point up –Sky is Clear
Term
Definition
 the collection of all possible events     –Red Card or Black Card   –The thumbtack lands in the point up or point down position   –Sky can be: Clear, Few Clouds, Many Clouds, Other
Term
 Definitions illustrated by Venn diagrams
Definition
 –Experiment, Event, Sample Space, Probability, Mutually exclusive events, Complement of an event, Conditional probability of A given B, Independent, Intersection, Union
Term
 The Probability of an event A
Definition
 denoted P(A) is a real number between 0 and 1 that indicates the likelihood that event A will occur when the experiment is performed.
Term
 The Complement of an event A
Definition
 denoted A´, is the event that A does not occur.
Term
 The Intersection of A and B
Definition
 the event that both A and B occur.
Term
 The Union of A and B
Definition
 the event that A or B occur   1.P(A or B) = P(A) + P(B) – P(A and B)
Term
 A and B are mutually exclusive events
Definition
 •means P(A ∩ B) = 0
Term
 The probability of A given B
Definition
 denoted P(A|B), is P(A ∩ B)/P(B)
Term
 A is Independent of B
Definition
 means P(A) = P(A|B) = P(A ∩ B)/P(B)   –Which implies that A and B are independent if and only if P(A ∩ B) = P(A) * P(B)
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