Statistics Unit 1 and Chapter 2 Key Vocabulary

Vocabulary flashcards covering key introductory statistics concepts, data classifications, sampling techniques, levels of measurement, frequency distributions, and critical evaluations.

Statistics

The science of collecting, analyzing, interpreting, and presenting data.

Data

The actual observed values of a variable.

Datum

The singular of data.

Descriptive Statistics

Methods used to organize, summarize, and display data.

Inferential Statistics

Uses sample data and probability to make conclusions or estimates about a population and judge how confident we are in those conclusions.

Probability

A mathematical tool used to study randomness and the likelihood of outcomes.

Population

The entire collection of people, objects, or things being studied.

Sample

A portion of the population selected to gain information about the whole population.

Parameter

A numerical characteristic of an entire population.

Statistic

A numerical characteristic of a sample; it is often used to estimate a population parameter.

Variable

A characteristic or measurement that can be determined for each member of a population.

Numerical Variable

A variable whose values are numbers representing counts or measurements, such as age, height, or income.

Categorical Variable

A variable whose values place individuals into groups or categories, such as eye color, major, or yes/no.

Quantitative Data

Numerical data representing an amount, count, or measurement.

Qualitative Data

Data that describe a category, quality, or attribute rather than an amount.

Discrete Data

Quantitative data that result from counting; usually separate, countable values.

Continuous Data

Quantitative data that result from measuring and can include decimals or fractions.

Representative Sample

A sample that has similar characteristics to the population it represents.

Simple Random Sample

A sample chosen so every possible group of individuals of the same size is equally likely to be selected.

Stratified Sample

Divide the population into groups called strata, then randomly sample from every group, often proportionally.

Cluster Sample

Divide the population into clusters, randomly select some clusters, then study everyone in the selected clusters.

Systematic Sample

Randomly choose a starting point, then select every nth individual.

Convenience Sample

A non-random sample made from individuals who are easiest or most readily available to reach.

Sampling With Replacement

After an individual or item is selected, it is returned and could be selected again.

Sampling Without Replacement

After an individual or item is selected, it stays out and cannot be selected again.

Sampling Error

Natural error or difference caused by using a sample instead of the entire population.

Non-Sampling Error

Error caused by factors unrelated to random sampling, such as confusing questions, inaccurate answers, or recording mistakes.

Sampling Bias

Occurs when some members of the population are more likely to be selected than others, causing the sample to favor certain groups.

Variation

Also called spread or dispersion; describes how spread out a set of data is.

Sample Size

The number of observations in a sample, often written as $n$. Larger representative samples generally reduce sampling variability, but they do not fix bias.

Self-Selected Sample

A sample in which people choose themselves to participate, which can create bias.

Nonresponse Bias

Bias that can occur when selected people do not respond, refuse, or leave a study.

Correlation

An association or relationship between two variables; correlation alone does not prove that one causes the other.

Causation

A relationship in which a change in one variable actually causes a change in another.

Confounding Variable/Event

An outside factor that affects the results and was not properly considered.

Level of Measurement

The way a set of data is categorized or measured.

Nominal Scale

Categories or labels only, with no meaningful order or ranking. Examples: eye color, car type, yes/no.

Ordinal Scale

Categories that can be ranked, but the differences between ranks are not necessarily equal or measurable.

Interval Scale

Ordered numerical data with meaningful, equal differences between values but no true zero. Example: temperature in °F or °C.

Ratio Scale

Ordered numerical data with equal differences and a true zero, so ratios are meaningful. Examples: height, weight, age, income, distance.

Frequency

The number of times a particular data value occurs.

Relative Frequency

The proportion or percentage of observations with a certain value; calculated as frequency divided by total sample size ($\frac{f}{n}$).

Cumulative Frequency

A running total of the frequencies up to and including a given value.

Cumulative Relative Frequency

A running total of the relative frequencies; shows the proportion or percent of observations at or below a given value.

Stem-and-Leaf Plot

A display that organizes numerical data by splitting each value into a stem (leading digit or digits) and a leaf (final digit).

Stem

The beginning digit or digits of a value in a stem-and-leaf plot.

Leaf

The last digit of a value in a stem-and-leaf plot.

Line Graph

A graph that plots data points and connects them with lines to show patterns or changes.

Bar Graph

A graph that uses separate bars to compare frequencies or values across categories or discrete values.

Critical Evaluation: Representativeness

Ask whether the sample accurately represents the population.

Critical Evaluation: Bias

Ask whether the study was designed or conducted in a way that favors a certain result.

Critical Evaluation: Sample Size

Ask whether the sample is large enough and representative enough to support reasonable conclusions.

Critical Evaluation: Undue Influence

Ask whether participants were pressured or influenced to answer in a certain way.

Critical Evaluation: Funding/Self-Interest

Consider who paid for the study and whether they could benefit from a particular result.

Critical Evaluation: Misleading Data

Check whether numbers, graphs, percentages, or wording are presented in a way that makes results look different from reality.