AP Stats Vocab

Statistics

the science of collecting, analyzing, and drawing conclusions

statistics

numerical quantities calculated from data that summarize or describe the data

Data

specific values along their context

Individual

a person, animal, or any thing described in a dataset

Variable

any attribute that can take different values for different individuals

Population

set of individuals with a common characteristic

Sample

A subset of the population being studied

Categorical variable

Variables that indicate what group or category each individual belongs to

Quantitative variable

Variables that contain measured numerical values and typically has a unit

Distribution

Tells us what values the variable takes and how often in takes them

Frequency table

Shows the number of individuals having each data value

Relative frequency table

Shows us the proportion/percent of individuals having each data value

Discrete

Variable that can take a countable number of values

Continuous

Variable that can take in infinitely many values

Resistant

when a measure of center or variability is not highly affected be extreme values

Median

Midpoint of the distribution (half of the data is smaller, and half is larger)

Mean

Average of all data values

Right-skewed

The mean is pulled toward the right tail

Left-skewed

The mean is pulled toward toward the left tail

Range

Distance between the minimum and maximum values

Standard deviation

The typical distance of the values in a distribution from the mean

Quartiles

Divide the data set into 4 equal groups

Outlier

A person, object, or data point that is significantly different, distant, or distinct from the main group, body, or average

Five number summary

Minimum, Q1, median, Q3, maximum

Percentile

The percent of data values less than or equal to a given value

Standardized score

Tells us the number of standard deviations a given value is above or below the mean

Normal distribution

a mound-shaped, unimodal, and symmetrical curve

Empirical rule

Within 1 standard deviation → 68%

Within 2 standard deviations → 95%

Within 3 standard deviations → 99.7%

Explanatory variable

May help predict or explain changes in a response variable

Response variables

Measures the outcome of a study

Association

If knowing the value of one variable helps to predict the value of the other

Correlation

A measure of the strength and direction of a linear relation between two quantitative variables

Census

Used to collect data from every individual in a population

Sample study

Aims to gather information about the population without disturbing the population

Experiment

Actively imposes treatment to measure the response

Observational study

Observes individuals and measures variables of interest, but does not attempt to influence the response

Convenience sample

Consists of individuals from the population who are easy to reach

Voluntary response

Consists of people who choose to be in the sample by responding to a general invitation

Random sample

Consists of individuals from the population who are selected for the sample using a chance process

Simple random sample (SRS)

a sample of size n is selected so that every possible group of n individuals has an equal chance of being selected

Stratified random sample

When the population is divided into groups called strata and some individuals are selected from every group to be sampled

Cluster sample

When the population is divided into groups called clusters and all individuals from some selected clusters are samples

Systematic random sample

Choose a random starting point and select every Kth individual after that point

Multistage sample

Uses random sampling at more than one stage

Bias

When the sample or data collection systematically favors certain outcomes

Undercoverage

Some groups in the population are left out of the process of being selected for the sample

Nonresponse

Respondents give inaccurate or false answers

Wording of questions

The wording of a question can influence the responses (leading questions can lead to response bias)

Sample frame

A list of individuals from which a sample will be drawn

Sampling variability

Different random samples of the same size from the same population produce different estimates

Inference

The process of drawing conclusions about a population based on the sample data