AP STATS UNIT 1-4

Categorical Variable

Variable that takes a name.

Quantitative Variable

Numerical values (makes sense to average)

Discrete Variable

Countable, finite. (0,1,2)

Continuous Variable

Not always exactly countable. (Weight)

What is S O C S

Shape, Center, Outliers, Spread

Skewed, Unimodal, Bimodal are examples of:

Shape

Values far from the mean

Outliers

Mean, Median are descriptions of:

Center

Range, IQR are descriptions of

Spread

“C” in CSOCS is for:

Context

Mean is:

Sum divided by number of values

Median is:

Middle value

Which is affected by outliers: Mean or Median?

Mean

Empirical Rule (FOR NORMAL DISTRIBUTIONS)

68% within 1SD, 95% Within 2SD, 99.7% within 3SD

IQR is:

Q3-Q1

Q1 is

25th percentile

Median (in terms of percentile) is

50th percentile

Q3 is

75th percentile

Five number summary:

min, q1, median, q3, max

Lower Outlier Rules (fence + SD)

q1-1.5 x IQR & mean - 2SD

Upper Outlier Rules (fence + SD)

q3 + 1.5 x IQR & mean + 2SD

Formula for Z Score:

(value - mean) / (standard deviation)

(Calculator Function) To find mean, standard deviation, and 5 number summary for a data set.

1 Var Stats

(Calculator Function) Finds the proportion of observations above, below, or between values assuming a normal model.

normalcdf (lower, upper, mean, SD)

(Calculator Function) Finds a value given a percentile.

invNorm(area, mean, standard deviation)

What is CDOFS

Context, Direction, Outliers, Form, Strength

r value is

correlation coefficient. is between -1 and 1

what doese’t affect r value?

changing units, switching axes

Correlation does not equal…..

causation

Equation of LSRL

y hat = a +bx

Equation for residual:

y (actual) - y (predicted) = residual

Positive/Negative residuals mean:

Positive = Underestimation, Negative = Overestimation

Interpretation of Slope

For every 1 unit change in independent variable, our model predicts and average change of the slope in response variable

explanatory variable

independent variable

response variable

dependent variable

interpretation of y intercept

when independent variable is zero, LSRL predicts dependent variable would be y intercept.

r² value is:

the precent of the variability in the dependent variable that can be explained by the linear relationship with the independent variable.

What value is the slope:

0.16292

What values is the y intercept

(Constant) 38257

What does it mean if the residual plot has a pattern?

LSRL is BAD

What does it mean if the residual plot dosen’t have a pattern?

LSRL is GOOD

How do I find correlation coefficient from r² ?

sqrt (r²)

(Calculator Function) Gives summary stats for both variables.

2-Var Stats (L1, L2)

(Calculator Function) Creates the least-squares regression line.

LinReg(ax+b) (L1, L2)

Simple random sample:

Random selected Subset of population.

Stratifed random sample

splits population into groups based on shared traits, choose some from each group

Cluster Sample

Splits population into groups, everyone from group gets chosen

Systematic Random Sample:

Picking individuals at regular/set intervals

Convenience Sampling

(bad sampling) choosing who is easy to each.

Voluntary Response Sampling

(BAD) allowing people to choose to participate.

Under coverage

When some people are left out.

Nonresponse

When individuals cant/dont respond

Response bias.

lying, but for a reason

Observational Study

Collecting data without influence of subjects

Experiment

Collecting data with influence of subjects

What is CRCR for experimental design

Comparison, Random Assignment, Control, Replication

Confounding Variable

When another variable affects the results.

Placebo

Fake Treatment

Single Blind

Subjects don’t know treatment, researchers do.

Double Blind

nobody knows who has what treatment.

Block

Group of experimental units with same characteristic

Block Design

subjects are divided based on specific characteristics

Matched Pair Design

Subjects are PAIRED.

Mutually Exclusive

two events that cannot occur at the same time

Independent Events

One dosen’t effect the other.

How to find the probability of either one of 2 mutually exclusive events happening?

Add them

How to find the probability of either one of 2 NON-mutually exclusive events happening?

Add them, subtract the overlap.

How to find the probability of 2 independent events BOTH happening?

multiply them.

How to find the probability of 2 NON-independent events BOTH happening?

Multiply the probability of the first event with the probability of 2nd event, given that the first has already happened.

How do i find the chance that an event simply dosen’t happen.

1 - Probability that the event happens.

Complement Rule

P(A^c) = 1-P(A)

Expected Value Formula

x times probability of x (1 × 1.0)

What changes when we add or subtract the same constant to each value in a probability distribution? (Shape, Center, Variability?)

Center (changes by the constant)

What dosen’t change when we multiply or divide the same constant to each value in a probability distribution? (Shape, Center, Variability?)

Shape.

What is BINS (for binomial distributions)

Binary, Independent, Number, Success.

(Calculator Function) Calculates probabilities using a known normal distribution.

normalcdf(lower, upper, mean, standard deviation)

(Calculator Function) Finds a value corresponding to a probability

invNorm(probability, mean, standard deviation)

(Calculator Function) Probability of exactly x successes.

binompdf(number of trials, probability of success, number of successes)

(Calculator Function) Probability of at most x successes.

binomcdf(number of trials, probability)

(Calculator Function) Probability first success occurs on trial x.

geometpdf(probability, x)

(Calculator Function) Probability first success occurs by trial x.

geometcdf(p, x)