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Unformatted text preview: Statistic A way of reasoning, along with a collection of tools and methods, designed to help us understand the world Categorical Variable A variable that names categories (whether with words or numerals) Quantitative Variable A variable in which the numbers act as numerical values. They ALWAYS have units. HISTOGRAMS dont display categorical data  BAR CHARTS dont display quantitative data. 1. Adding (or subtracting) the same number to each data value in a variable shifts all measures of center mean, median, midrange  by the amount added (or subtracted) 2. Adding (or subtracting) the same number to each data value does not change measures of spread SD, IQR, range. 3. IF SYMMETRIC then MEAN= MEDIAN RANGE Difference between the lowest and highest values, Range= max min Resistant A calculated summary is said to be resistant if it is affected only a limited amount by outliers. The Normal model is a special, unimodal , and symmetric probability model. It is characterized by its mean and Standard Deviation. about 68% of the values fall within 1 standard deviations of the mean 95% of the values fall within 2 standard deviations of the mean. 99.7%  almost all of the values fall within 3 standard deviations of the means A.K.A the 689599.7 Rule. Probability models are a concise way to describe the overall pattern of a distribution. Any model lies above the HORIZONTAL axis and has an AREA OF ONE The median has half the area of the probability model on either side The mode is the peak of the model The mean is the balance point Standardizing Data Standardizing uses the standard deviation as a ruler to measure distance from the mean, creating zscores. We standardize to eliminate units. Using zscores, we can compare apples and oranges values from different distributions or values based on different units. Zscore can identify unusual or surprising values among data. ZScore Tells how many standard deviations a value is form the mean; zscores have a mean of zero and a standard deviation of one. A zscore between 1 and 1 is uncommon, but a zscore of plus or minus 3 is more rare. Any higher number calls for attention. 5 number summary The extremes (min and max), Quartiles Q1 and Q3, and the median. ONCE we have the five summaries, we can display a bloxplot.  IQR = Q3 Q1  Upper fence = Q3 1.5(IQR) Lower fence = Q1 1.5(IQR) Range = Max Min When comparing or describing distributions of several groups, consider there: SHAPE (Modes Unimodal, Bimodal, Multimodal) (No mode = Uniform) CENTER (Determine the Mean, Symmetric, Skewed, Always mention Outliers) SPREAD (IQR and SD) Association Between two quantitative variables: Direction : A positive direction or association means that as one variable increases, so does the other. When increases in one variable generally correspond to decreases in the other, the association is negative Form : The form we care about is straight, but you should certainly describe other patterns you see in scatter plots.The form we care about is straight, but you should certainly describe other patterns you see in scatter plots....
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 Spring '07
 VELLEMANP

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