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The collection, presentation, and description of sample data 


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Interpreting the values that result from the descriptive techniques and making decisions and drawing conclusions about the population. 


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The science of collecting, describing, and interpreting data 


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A collection, or set, of individuals or objects or events whose properties are to be analyzed. 


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When the membership of the population can be physically listed 


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When the membership of the population is unlimited 


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Variable (or Response Variable) 

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A characteristic of interest about each individual element of a population or sample 


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The value of the variable associated with one element of a population or sample. This value may be a word, a number, or a symbol.
Ex. Bill entered college at age "23" 


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The set of values collected for the variable from each of the elements that belong to the sample. 


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A planned activity whose results yield a set of data 


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A numerical value summarizing all the data of an entire population 


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A numerical value summarizing the sample data 


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Qualitative, or Attribute, or Categorical Variable 

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A variable that describes or categorizes an element of a population 


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Quantitative, or Numerical Variable 

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A variable that quantifies an element of a population 


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A qualitative variable that categorizes (or describes, or names) an element of a population. Not only are arithmetic operations not meaningful for data that result from a nominal variable, but also an order cannot be assigned to the categories 


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A qualitative variable that incorporates an ordered position, or ranking 


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A quantitative variable that can assume a countable number of values. Intuitively, the discrete variable can assume the values corresponding to isolated points along a line interval. That is, there is a gap between any two values
Ex. counting 


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A quantitative variable that can assume an uncountable number of values. Intuitively, the continuous variable can assume any value along a line interval, including every possible value between any two values
Ex. measuring 


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Measures of Central Tendency 

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Mode, mean, median, midrange 


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A histogram is a frequency graph that depicts the frequency distribution of a quantitative variable 


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Use when one value is "worth" less (x2 in your sample than normal society) 


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(xmin + xmax) / 2 Midrange – middle of the data set 


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the middle number (half the area of the curve) when data are ranked according to size
As soon as there is a big difference between the mean and median, you know you have skew in your data (either left or right) 


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which value occurred the most times 


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You can make more meaningful comparison between two xvalues that came from separate populations. An x's zscore defines how many standard deviations from the mean the xvalue is.
z = (value  mean) / st. dev. 


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68.3% of observations will lie within 1 standard deviation from the mean (~15.6% in each tail) 95.4% of observations will lie within 2 standard deviations from the mean (~2.3% in each tail) 99.7% of observations will lie within 3 standard deviations from the mean (~0.15% in each tail) 


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probability of A = number of time A occurred / number of trials 


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probability of A = number of times A occurs in a sample space / number of elements in sample space 


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found by dividing the class frequency by the total number of observations 


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As the number of trials goes up, the observed relative frequency (empirical probability) will tend to approach the theoretical probabiltiy 


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The list of all possible outcomes of the experiement 


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P(AB) = P(A n B) / P(B) n = intersection, include all events that are in both A and B 


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Probability Models Stochastic process  random. Sometimes there's predictability about the pattern, not the variable. 


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a random process with only two outcomes: "success" x=1 or "failure" x=0 
A Bernoulli process gives rise to the binomial distribution. What is the random variable that has a binomial distribution? x = number of successful trials What is the range of x? n  0 


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when we make inferences about a population whose elements are all known, they are not inferences  we know all the possibilities 


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Independent vs. Dependent Events 

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If you compare marginal and conditional probability, you can see that you have independent or related events. If the numbers are the same, it means that they have nothing to do with each other. If the numbers are radically different, then you have related events. 


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every value appears with equal frequency 


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Values of the variable that divide s aset of ranked data into 100 equal subsets; each set of data has 99 percentiles. The kth percentile, Psubk, is a value such that at most k% of the data are smaller in value than Psubk, and at most (100k)% of the data are larger 


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The pattern of variability displayed by the data of a variable. The distribution displays the frequency of each value of the variable 

