AP Stats - FULL REVIEW

Descriptive statistics

Descriptive statistics

methods of organizing and summarizing statistics

Inferential statistics

making generalizations from a sample to the population

population

an entire collection of individuals or objects

Sample

a subset of the population selected for study

Variable

any characteristic whose value changes

Data

observations on single or multi-variables

Categorical variables

Qualitative

basic characteristics

Numerical variables

Quantitative

measurements or observations of numerical data

Discrete data

listable sets (counts)

Continuous data

any value over an interval of values (measurements)

Univariable

one variable

Bivariate

two variables

multivariate

many variables

Symmetrical distribution

Data on which both sides are fairly the same shape and size

"Bell curve"

Uniform

every class has an equal frequency (number)

"Rectangle"

Skewed

One side (tail) is longer than the other side

The skewness is in the direction that the tail points

Bimodal

data of two or more classes have large frequencies separated by another class between them

"double hump camel"

How to describe numerical graphs

S: shape - overall type (symmetrical, skewed, uniform, bimodal)

O: outliers - gaps, clusters, etc.

C: center - middle of the data (mean, median, mode)

S: spread - refers to variability (range, standard deviation, IQR)

C: context - EVERYTHING must use CONTEXT

Parameter

a value of a population (typically unknown)

Statistic

a calculated value about a population from a sample(s)

Measures of center

mean, median, mode

Median

the middle point of the data (50th percentile) when the data is in numerical order.

*if two values, average them

Mean

μ for population (parameter)

x̄ for sample (statistic)

Mode

occurs the most in the data

Can be more than one, or none if all data points occur once

Variability

allows statisticians to distinguish between usual and unusual occurrences

Measures of spread

range, IQR, standard deviation

Range

a single value

max-min

IQR

interquartile range

Q3-Q1

Standard deviation

σ for population (parameter)

s for sample (statistic) - divided by df

measures the typical or average deviations from the mean

Variance

standard deviation squared

Resistant

affected by outliers

Median, IQR

Non-resistant

NOT affected by outliers

mean, range, variance, standard deviation, correlation coefficient, LSRL, coefficient of determination

comparison of mean & median based on symmetrical graph

equal

comparison of mean & median based on skewed right graph

mean is larger

comparison of mean & median based on skewed left graph

mean is smaller

Trimmed mean

use a % to take observations away from the top and bottom of the ordered data

can possibly eliminate outliers

linear transformations of mean and st dev

mean changed by addition, subtraction, multiplication, division

standard deviation changed by multiplication & division

Combination of two or more random variables

Just add or subtract means

Add variances and square root for st dev - X and Y MUST be INDEPENDENT

Z-Score

a standardized score

tells you how many standard deviations from the mean an observation is

in normal distribution, it creates a normal curve consisting of z-scores with a μ=0 & σ=1

Z=(x-μ)/σ

Normal curve

a bell shaped and symmetrical curve

as σ increases the curve flattens

as σ decreases the curve thins

Empirical rule

normal curves

68% of population is between -1σ and 1σ

95% of population is between -2σ and 2σ

99.7% of population is between -3σ and 3σ

Boxplots

5 number summary

min, Q1, median, Q3, max

Probability rules - Sample space

collection of all outcomes

probability of sample space is 1

Probability rules - Event

any sample of outcomes

Probability rules - Complement

all outcomes not in event

P+ (1 - P) = 1

Probability rules - Union

A or B

all the outcome in both circles

P(A) + P(B) - P(A&B)

Probability rules - Intersection

A and B

happening in the middle of A and B

P(A) x P(B) if A&B are independent

Probability rules - Mutually exclusive (disjoint)

A and B have no intersection - CANNOT happen at same time

Probability rules - Independent

if knowing one event does not change the outcome of another

Probability rules - Experimental probability

the number of success from an experiment divided by the total amount from the experiment

Probability rules - Law of large numbers

as an experiment is repeated the experimental probability gets closer and closer to the true probability

the difference between the two probabilities will approach 0

All probability values must add up to

1

P (at least 1 more)

1 - P(none)

conditional probability

takes into account a certain condition

A given B

(P(A&B)) / P(B) = P(both) / P(given)

correlation coefficient (r)

a quantitative assessment of strength and direction of a linear relationship

[-1, 1] = 0, no correlation

(0 ± 0.5) = weak

(±0.5 ± 0.8) = moderate

(±0.8 ± 1) = strong

Least Squares Regression Line (LSRL)

ŷ = a + bx