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
don’t display categorical data 
BAR CHARTS
don’t 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.
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 Spring '07
 VELLEMANP
 standard deviations, Response bias, large city school

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