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Reasons to Sample over census
 cheaper
 quicker
 large populations may be inaccessible
 destructiveness of the observation
 carefully obtained sample is better than sloppily conducted census

Sampling Error
 due solely to particular units that have been selected
 chance
 sampling bias(usually the result of poor planning)

Protection Against Sampling Error
 chance>use a large enough sample
 sampling bias>have a good plan

Non Sampling Error
 can occur in census or sampling
 results solely from the manner in which observations are made
 ex. inacurate measurement from malfunctioning instruments

Types of Sampling(list)
 convenience
 representative
 random(with and without replacement)

Convenience Sampling
 usually self selected (people that phone in to give opinion)
 bad type of sampling
 results regarded with caution

Representative Sampling
 represent the characteristics of a population as closely as possible
 more reliable than convenience

Random Sample
 most important type of sample
 people recruited for use are totally random(can be with or without replacement)

Canadian Census
 every 5 years
 last one was May 10, 2011
 employ about 34,000 temp workers for it
 must be filled out by law
 first one taken in 1871(had 211 questions)

Agriculture Census
 started in Manitoba in 1896, Sask and Alberta joined in 1906
 every 5 years
 separate from regular census

Element
specific subject(object) about which the info is collected

Variable
characteristic under study for each element

Observation/measurement/data value
value OF a variable FOR an element

Data/Data set
collection of observations on one or more variables

Quantitative Variables
 can be measured numerically
 math can be performed on the results
 can be continuous or discrete

Continuous Variables
 variable that can assume any numerical value
 blood pressure, time, distance

Discrete Variables
 countable units
 you can have 3 dogs, but not 2.3 dogs
 the variable cannot assume any number in its range, only full units

Qualitative Variables
must be defined in nonnumerical categories

Raw Data
data recorded in the sequence in which it was collected

Frequency Distribution
lists the number of the data occurrences for each category of data

Relative Frequency Distribution
shows the percent of observations that belong to each category

Pareto Chart
bar graph that shows the bars in decreasing order of frequency (can be frequency or relative frequency)

Continuous Histograms
similar to bar graph, but no gaps between the bars

Discrete Histograms
similar to bar graph but does have gaps between the bars (versus continuous)

Parameter
descriptive measure of a population

Statistic
descriptive measure of a sample

Mean
 average of the data
 can be of sample or population

Median
 the middle term of data points that have been arranged in a ranked order (increasing or decreasing)
 if you have an even number of terms, average the 2 middle terms

Mode
 the number which occurs with the highest frequency
 can be unimodal, bimodal or multimodal
 only measure of central tendency for qualitative data

Range
 difference between the highest and lowest data points
 influenced by outliers

Standard Deviation
 tells you how closely the values of the data set are clustered around the mean
 low value= data is closer to mean than a large SD
 calculated by taking the square root of the variance
 always in same unit as data
 can never be negative, may be zero

5 Number Summary
include the lowest value, quartile 1 boundary, median, quartile 3 boundary and highest value

law of large numbers
 the long run relative frequency of repeated independent events gets closer to the relative true frequency as the number of trials increases
 the more times you flip a coin the closer you will get to 50/50 results

Sample Space
the set of all possible outcomes of the experiment

Event
 any collection of outcomes from an experiment
 denoted using capital letters such as A

Simple Event
includes only one of the final outcomes for an experiment and is denoted E_{i
}can only be achieved one way

Compound Event
 collection of more than one outcome for an experiment
 can have multiple ways of achieving the requirement

Classical Probability
done when all outcomes from an event are equally likely

Relative Frequency Probability
used when all possible outcomes do not have an equal chance to occur

Subjective Probability
probability assigned to an event based on subjective judgement (experience, information and belief)

Marginal Probability
 probability of an event without considering any other event
 also called simple probability

Conditional Probability
probability that an event will occur given than another event has already occured

Mutually Exclusive Events
 events that cannot occur together
 events have no shared elements
 in a venn diagram the circles will not overlap

Mutually Non Exclusive Events
where observing one thing does not rule out the other, they can both occur, or one or the other

Complimentary Events
two always mutually exclusive events that taken together include all the outcomes for an experiment

