AP Stats Unit 1

Statistics

Studies concerning data collection, organization, analysis, interpretation, and presentation

Statistic

Calculation made from data

Data

Systematically recorded information with corresponding context

Variable

Characteristic differing from one subject to another

Two types of Variables

Quantitative and Categorical

Two types of Quantitative Variables

Discrete (Whole #s)

Continuous (Anything with a decimal)

Frequency v Relative Frequency

Raw numerical values vs. Percentages/Proportions

Ways to represent Categorical Data

Charts- Pie, Bar, Side By Side Bar Chart

Tables- Frequency/Rel. Frequency Tables

Ways to represent Quantitative Data

Dot Plot

Stem/Leaf Plot

Histogram

Three Distributions of Graphs: uniform, unimodal, and bimodal

Three Skews of Graphs: Skew left, skew right, symmetric

Note how skew affects where mean and median will be

What is the appropriate acronym for describing a distribution?

SOCCS

S- Shape (Distribution/Skew)

O- Outliers/Unusual features (Gaps)

C- Context

C- Center (Mean, Median)

S- Spread (Range [Max-Min], IQR)

Mean

Average (Sum of all terms / # of terms)

Median

Exact middle number within a set

i.e {4,6,9,11,12}

Q1/Q3

Exact middles of the lower/upper halves of a data set

{1,2,3,4,5,6,7}

IQR

Q3-Q1

Represents the spread of the middle 50% of the data set

Sx/Standard deviation

Average distance each value is from the mean

What are the two ways to calculate outliers?

1.5 x IQR

Mean ± 2Sx

Nonresistant vs Resistant

Affected by outliers (Mean, Sx, Range) vs

Not affected by outliers (Median, IQR)

What values make up a 5-number summary?

Minimum, Q1, Median, Q3, Maximum

Boxplots’ Demonstration of Skew

Percentile

Percent of values less than or equal to the given number

Z-Score

How many standard deviations above or below the mean a given value is

(Individual value - Mean)/Standard deviation

Memorize the percents of the mean ± Standard deviations on a normal model

Important Calculator functions

Probability that a specified variable falls within a certain range:

Normalcdf: (Min, max, mean, standard deviation)

Finding an exact point along the curve:

Normalpdf: (Given point, mean, standard deviation)

Finding a point given its percentile:

InvNorm: (Percentile in decimal form, mean, standard deviation)