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STAT 2040
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Gary Umphrey
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Final

# Stats Cheat Sheet.docx

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University of Guelph

Statistics

STAT 2040

Gary Umphrey

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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