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Final

# Stats Cheat Sheet.docx

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School
University of Guelph
Department
Statistics
Course
STAT 2040
Professor
Gary Umphrey
Semester
Fall

Description
Monty Hall Prob: chance you pick the right door, if you Quartiles: arrange in ascending order, Q is med1an of top half of observations and Q is 3ottom half, IQR switch, chance of winning becomes . (interquartile range) = Q – 3 [not1sensitive to Population (who you apply findings to in real life) vs. outliers], Sample (subset of population, random [each has same Boxplots: calculate 3 quartiles and IQR, draw line chance of being picked for study]) representing scale of measurement, draw box with Parameters (numbers that characterize population 2 ends of box at Q a1d Q , d3aw line through box at vs. Statistics (characterize sample x, S, S ) median, calculate inner fences [ Descriptive: describe data ], draw whiskers Inferential: use info in sample to see says about from box to observation closest to & still within inner population fences, anything else is outlier, no way of knowing Multivariate: measuring multiple variables, Bivariate (2 how many observations are in Q and whiskers from variables), Univariate (1 variable) boxplot Categorical variable (qualitative) vs. Numerical (quant.) Percentile: the k-th percentile is the value of the Observational Studies (observe response for specific variable such that k% of the observations fall below th variable for each individual) vs. Experimental that value, 50 percentile (median), easiest to read off (investigate effects of certain conditions on individ.) of cumulative relative frequency polygon (go up to Statistical Inference: claim, experiment, likelihood (how .06, to line, down to see value that 60% fall under) likely it is that experimental outcome occurs given that the Linear Transformations: , mean, median claim is true), conclusion and mode must be multiplied by b and added by a, Discrete: set of all possible values is finite (counting) range and S must be multiplied by b, S must be Continuous: set of all values is interval (measuring) multiplied by b 2 Countably Infinite: infinitely many values but countable Chebyshev’s Theorem: given a number “k” ≥ 1 and Frequency Distribution: choose range, divide into non- set of “n” observations, at least of the overlapping equal parts (approx. √ classes), count measurements will fall within “k” standard deviations number of observ. in each interval, ties are assigned to upper class, (Frequency [ f] = n), Relative Frequency of the mean, at least 0.75 within 2 std.’s and at least 0.89 within 3 std.’s, “k” does not have to be an integer, (ri = , r of class = i(class) – Fi- impossible to violate unless you make calculating errors 1(previous class), , Cumulative Frequency (F) = i sum of all f’s in classes so far including its own, Relative Empirical Rule: for a distribution that is approx. bell Cumulative Frequency (R) = i or sum up r vilues up to curved or normal, about 68% of observations will fall within 1 std., about 95% within 2 std.’s and about all i within 3 std.’s Frequency Histogram: plot frequency vs. class intervals; relative frequency histogram will have same shape, Z Scores: always have a mean of 0 and a std. of̄1, to convert observations to z scores, , z score of different y-axis values (values on both sides will = same x) Frequency Polygon: connect the midpoints, can have 1 observation gives number of standard deviations shape graph that tells us 4 things away from the mean and +/- indicates direction Unimodal (one mode), Bimodal (2 modes) Summary Statistics for Grouped Data: need to find Positively Skewed (skewed to left, long tail on right) midpoints for each class, ̄ Negatively Skewed (skewed to right, long tail on left) ( ) Measures of Central Tendency: indicate where majority ̄ ̄ of data is centered (arithmetic mean [not good measure if Sample Space: listing of all possible outcomes S={} there are outliers, x on calc], median [good for avg. of Simple Event: consists of exactly one outcome, an skewed data, x>median in + skewed, x
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