AP Statistics Vocabulary

Population

entire group being studied

Sample

subset of the population used to draw conclusions

Parameter

numerical summary of a population

Statistic

numerical summary of a sample

Descriptive statistics

methods of organizing and summarizing data

Inferential statistics

methods of using sample data to make conclusions about a population

Categorical variable

variable that places data into categories

Quantitative variable

variable measured with numbers

Frequency

number of times a value appears

Relative frequency

proportion of times a value occurs

Distribution

pattern of variation of a variable

Outlier

value that lies far outside the overall pattern

Center

typical value such as mean or median

Spread

measure of variability such as range IQR or standard deviation

Skewed left

tail is longer on the left side

Skewed right

tail is longer on the right side

Symmetric

both sides of the distribution are roughly mirror images

Mean

average of values

Median

middle value of a data set

Mode

value that occurs most frequently

Range

difference between largest and smallest values

Interquartile range

difference between Q3 and Q1

Standard deviation

average distance of values from the mean

Variance

square of the standard deviation

Z score

number of standard deviations a value is from the mean

Normal distribution

symmetric bell

Empirical rule

in normal distribution about 68 percent 95 percent and 99.7 percent of data falls within 1 2 and 3 standard deviations respectively

Percentile

value below which a given percent of observations fall

Scatterplot

graph showing relationship between two quantitative variables

Correlation

strength and direction of a linear relationship between variables

Least squares regression line

line that minimizes the sum of squared residuals

Residual

difference between observed and predicted value

Extrapolation

predicting outside the range of data

Experiment

study where a treatment is imposed

Observational study

study where no treatment is imposed

Confounding variable

variable that influences both explanatory and response variables

Random assignment

assigning subjects to treatments by chance

Control group

group that receives no treatment or standard treatment

Placebo

fake treatment used in experiments

Double blind

neither subjects nor experimenters know who receives treatment

Blocking

separating subjects into groups before random assignment to reduce variability

Matched pairs design

experimental design where subjects are paired and each receives different treatments

Sampling

process of selecting a subset from the population

Simple random sample

every individual has an equal chance of being selected

Stratified random sample

population divided into groups then random sample taken from each group

Cluster sample

population divided into clusters then entire clusters are randomly selected

Systematic sample

every nth individual is selected

Bias

systematic error that favors certain outcomes

Voluntary response bias

people choose to respond often with strong opinions

Undercoverage

some groups are left out of the sample

Nonresponse bias

individual chosen for the sample does not respond

Response bias

inaccurate responses due to wording or behavior

Sampling variability

natural variation between different samples

Null hypothesis

statement of no effect or no difference

Alternative hypothesis

statement of an effect or difference

P value

probability of observing the data if the null hypothesis is true

Significance level

threshold for rejecting the null hypothesis usually 0.05

Type I error

rejecting a true null hypothesis

Type II error

failing to reject a false null hypothesis

Power

probability of correctly rejecting a false null hypothesis

Confidence interval

range of values believed to contain the population parameter

Margin of error

range above and below the sample statistic in a confidence interval

T distribution

used when population standard deviation is unknown

Chi square test

test used with categorical data to test independence or goodness of fit

ANOVA

analysis of variance used to compare more than two means

Binomial distribution

probability distribution for a fixed number of independent trials with two outcomes

Geometric distribution

probability distribution for number of trials until first success

Law of large numbers

as sample size increases sample mean approaches population mean

Central limit theorem

sampling distribution of sample mean is approximately normal if sample size is large

Simulation

method of modeling chance behavior to estimate probabilities