Introductory Statistics, Frequency Distributions, and Central Tendency Vocabulary

Vocabulary flashcards generated from introductory statistics lectures, covering statistical basics, research methods, frequency distributions, scales of measurement, distribution shapes, and central tendency measures.

Statistics

A set of mathematical procedures for organizing, summarizing, and interpreting information.

Population

The set of all individuals of interest in a study.

Sample

A set of individuals selected from the population, usually intended to represent it.

Variable

A characteristic or condition that changes or has different values among individuals.

Datum

A single measurement or observation.

Data

Plural of datum; a collection of measurements or observations.

Data Set

A collection of measurements or observations.

Parameter

A value, usually numerical, that describes a population.

Statistic

A value, usually numerical, that describes a sample.

Descriptive Statistics

Statistical procedures used to summarize, organize, and simplify data.

Inferential Statistics

Statistical techniques used to study a sample and make generalizations about the population from which the sample was selected.

Sampling Error

The naturally occurring discrepancy between a sample statistic and the corresponding population parameter.

Descriptive Research

A type of research whose purpose is to describe individual variables as they naturally exist.

Correlational Method

A research method where two variables are measured to examine whether a consistent pattern or relationship exists between them.

Experimental Method

A research method that demonstrates a cause-and-effect relationship between two variables through manipulation and control.

Manipulation

An experimental technique where the researcher changes the value of one variable from one level to another.

Control

Exercising authority over the research situation to ensure that extraneous variables do not influence the relationship being examined.

Random Assignment

A procedure where each participant has an equal chance of being assigned to each treatment condition, aiming to distribute participant characteristics evenly across groups.

Matching

A control method used to ensure equivalent groups or environments by balancing participant characteristics across groups (e.g., ensuring every group has 60% females and 40% males).

Holding Variables Constant

A control technique of keeping specific participant or environmental variables identical across groups (e.g., using only 10-year-old boys as participants).

Independent Variable

The variable that is manipulated by the researcher in an experiment.

Dependent Variable

The variable observed to assess the effect of the treatment in a study.

Control Condition

The group or condition in an experiment that does not receive the experimental treatment.

Experimental Condition

The group or condition in an experiment that receives the experimental treatment.

Non-Equivalent Groups Study

A nonexperimental study comparing two groups of scores where researchers have no ability to control which participants go into which group.

Pre-Post Study

A nonexperimental study where the same variable is measured twice for each participant, once before a condition and once after.

Quasi-Independent Variable

The variable used to create groups in nonexperimental research that is not manipulated by the researcher.

Construct

An internal attribute or characteristic that cannot be directly observed but is useful for describing and explaining behavior.

Operational Definition

A procedure that identifies a measurement procedure for measuring a construct and defines the construct based on the resulting measurements.

Discrete Variable

A variable consisting of separate, indivisible categories where no values can exist between neighboring categories.

Continuous Variable

A variable that can have an infinite number of possible values between two observed values.

Nominal Scale

A scale of measurement where categories have different names, are not systematically related, and function as classification by name.

Ordinal Scale

A scale of measurement with categories arranged in an ordered sequence, indicating ranking or relative magnitude.

Interval Scale

A scale of measurement with ordered categories separated by equal-sized intervals and an arbitrary zero point.

Ratio Scale

A scale of measurement with ordered, equal-sized intervals and an absolute zero point representing a complete absence of the variable being measured.

Raw Scores

The original, unchanged scores obtained in a study, represented by the symbol $X$.

$$N$$

The statistical symbol representing the total number of scores in a population.

$$n$$

The statistical symbol representing the total number of scores in a sample.

$$\Sigma$$

The summation sign used in statistical notation to mean 'the sum of'.

Frequency Distribution

An organized tabulation showing the number of individuals located in each category of a measurement scale.

$$\Sigma f X$$

The sum of scores obtained by multiplying each score ($X$) by its frequency ($f$) and adding the resulting products.

Proportion

The fraction of the total group associated with each score, calculated as $p = \frac{f}{N}$; also called relative frequency.

Grouped Frequency Distribution

A frequency distribution table where individual scores are grouped into class intervals.

Abscissa

The horizontal axis ($X$-axis) of a frequency distribution graph.

Ordinate

The vertical axis ($Y$-axis) of a frequency distribution graph.

Histogram

A frequency distribution graph for interval or ratio data that uses touching bars to represent frequencies.

Polygon

A frequency distribution graph that uses dots above each score to represent frequency, connected by continuous lines extending down to the $X$-axis at both ends.

Modified Histogram

A frequency distribution graph that uses a stack of blocks where each block represents one individual, making a vertical frequency scale unnecessary.

Bar Graph

A frequency distribution graph used for nominal and ordinal data that features spaces between bars to indicate distinct categories.

Symmetrical Distribution

A distribution shape where one side is approximately a mirror image of the other side.

Skewed Distribution

A distribution where scores pile up toward one end and gradually taper off toward the other end.

Positive Skew

A distribution where the tail tapers off toward the right or positive direction.

Negative Skew

A distribution where the tail tapers off toward the left or negative direction.

Percentile Rank

The percentage of individuals in a distribution with scores at or below a particular value.

Cumulative Frequency ($cf$)

The total number of individuals who have scores at or below a particular score, calculated by summing frequencies from the lowest score upward.

Cumulative Percentage

The percentage of individuals located at or below each score or category in a distribution.

Real Limits

The boundaries between scores on a continuous number line, located halfway between adjacent scores.

Interpolation

A mathematical process used to estimate intermediate values not directly reported in a frequency distribution table, based on the assumption of a constant rate of change across an interval.

Stem-and-Leaf Display

A tabular display that separates each score into a stem (first digit or digits) and a leaf (final digit), allowing identification of every individual score.

Central Tendency

Statistical measures used to identify a single score that represents the center or typical value of a distribution.

Mean

The arithmetic average of a set of scores, calculated by dividing the sum of all scores by the total number of scores.

Equal-Sharing Definition

An understanding of the mean as the amount each person would receive if the total were divided equally among all individuals.

Balance-Point Definition

An understanding of the mean as a point where the total distances of scores below it equal the total distances of scores above it.

Weighted Mean

The overall mean calculated when combining groups with different numbers of scores, computed as $M = \frac{\Sigma X_1 + \Sigma X_2}{n_1 + n_2}$.

Median

The midpoint of an ordered distribution that divides the scores into two equal-sized groups.

Mode

The score or category occurring with the greatest frequency in a distribution.

Unimodal Distribution

A frequency distribution that has only one mode.

Bimodal Distribution

A frequency distribution that has two modes.

Multimodal Distribution

A frequency distribution that has more than two modes.

Rectangular Distribution

A distribution with no mode because all values occur with the exact same frequency.

Open-Ended Distribution

A distribution that has no upper or lower limit for one of its categories, preventing the calculation of a sum of scores or a mean.