AP Statistics: Key Concepts and Formulas for Variables, Distributions, and Outliers

p-hat

Sample proportion (statistic)

p

Population proportion (parameter)

X-bar

Sample mean (statistic)

mu

Population mean (parameter)

p-hat1 - p-hat2

Difference in sample proportions

p1 - p2

Difference in population proportions

categorical variable

Qualitative, represents categories

quantitative variable

Numeric values

explanatory variable

A variable that explains response variable

symmetric distribution quartiles

Q3 - Q2 = Q2 - Q1

skewed right distribution

Q3 - Q2 > Q2 - Q1

skewed left distribution

Q3 - Q2 < Q2 - Q1

bar chart variable type

Quantitative

histogram variable type

Categorical

statistic

Numerical characteristics of a sample (X-bar, p-hat)

parameter

Numerical characteristics of a population (mu, p)

sample standard deviation formula

s = sqrt( Σ(xi - x̄)^2 / (n - 1) )

sigma

Population standard deviation

z-score formula

z = (data value - mean) / SD

Q1

25th percentile

Q2

50th percentile (median)

Q3

75th percentile

5-number summary

min, Q1, Q2, Q3, max

lower fence formula

Q1 - 1.5 × IQR

upper fence formula

Q3 + 1.5 × IQR

range formula

max - min

IQR formula

Q3 - Q1

mean>median

skewed right

mean

skewed left

q3-q2

left skewed

q3-q2>q2-q1

right skewed

response variable

what you’re trying to explain

experiment

can infer causation

observational study

only correlation, not causation

graphs with one quantitative variable 

histogram, dot plot

symmetric

mean = median

skewed right

mean>median

skewed left

mean<median

bimodal

2 peaks

mean

sensitive to outliers (use for symmetric)

median

resistant to outliers (use for skewed data)

boxplot

visual summary of 5 number summary

upper fence

Q3 + 1.5 xI QR

lower fence

Q1 - 1.5 x IQR

scatter plot

2 quantitative variables

strength of correlation

how close points lie to a line

Negative regression line

-1

positive regression line

1

correlation

the closer it is to 1, the stronger the correlation

purpose of linear regression

predicts the relationship between explanatory and response

confidence intervals

sample statistics vary from sample to sample

higher confidence

wider interval

95% correlation mean 

mean ± 2(SE)

SE

standard deviation/sqrt of sample size

bootstrap

for 95%, cut of lower and upper 2.5% of statistics

r

sample correlation

p (rho)

population correlation