Chapter 4: Data Management Statistics Vocabulary

Vocabulary flashcards defining foundational statistical terms, measurement scales, measures of central tendency, measures of variability, relative position measures, and normal distributions based on Chapter 4 notes.

Statistics

The science of collecting, organizing, and summarizing recorded information or data (descriptive statistics) in such a way that valid conclusions and meaningful predictions can be drawn from them (inferential statistics).

Descriptive Statistics

Methods concerned with the collection, description, and analysis of data without drawing conclusions or inferences about a larger set.

Inferential Statistics

Methods that utilize sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data.

Variable

A specific characteristic or attribute of a subject that may assume two or more different values.

Qualitative Variables

Variables whose values are measured not in terms of numbers, but categorically by means of expression or description.

Quantitative Variables

Variables that are always associated with numbers or a scale measure.

Nominal Scale

A measurement scale characterized by data consisting of names, labels, codes, or categories only, which cannot be arranged in an ordering scheme and cannot be used for calculations.

Ordinal Scale

A measurement scale involving data that may be arranged in some specific order or ranking.

Interval Scale

A scale of measurement where the difference between numerical values is meaningful, but there is no true zero point representing complete absence.

Ratio Scale

A scale of measurement where data are ordered by amount, equal differences represent equal attributes, and zero represents a true absence of the attribute.

Population

The entire set of all objects or subjects under statistical study.

Sample

Any subset of a population selected to collect data and project trends for the whole population.

Data Point

An individual element or single recorded score within a set of collected raw data.

Frequency Distribution Table (FDT)

A table listing all data points or group intervals alongside their frequency ($f$) and relative frequency percentage.

Histogram

A bar graph depicting grouped interval data where bar heights correspond to frequencies and bar widths match class interval sizes.

Pie Chart

A circular statistical graphic divided into slices representing relative frequencies to visually display proportions of categorical data.

Measure of Central Tendency

A single value indicating where the center of a distribution tends to be located, serving as a summary average.

Mean

The arithmetic average of a dataset, calculated as the sum of all data points divided by the total number of data points ($\bar{x} = \frac{\sum x}{n}$).

Median

The middle value separating an ordered numerical array of data points into two equal halves.

Mode

The specific data point or value that occurs most frequently within a dataset.

Measure of Variability

A statistical quantity measuring the degree of spread or dispersion of scores about the mean in a distribution.

Range

The difference between the highest value and the lowest value in a dataset ($R = \text{Highest Value} - \text{Lowest Value}$).

Deviation

The difference between an individual data point and the mean of the dataset ($x - \bar{x}$).

Variance

The mean of the squared deviations of data points from the sample mean, given by $s^2 = \frac{\sum (x - \bar{x})^2}{n - 1}$.

Standard Deviation

The positive square root of the variance ($s = \sqrt{s^2}$), providing a relative measure of the dispersion of data.

Percentile

A measure of position indicating the percentage of data falling below a given score, dividing a distribution into 100 equal subgroups.

Decile

A measure of relative position that splits an ordered distribution into 10 equal subgroups ($D_1$ through $D_9$).

Quartile

A measure of relative position that splits an ordered distribution into 4 equal subgroups ($Q_1$, $Q_2$, and $Q_3$).

Normal Distribution

A continuous, bell-shaped probability distribution symmetric about the mean, where mean, median, and mode coincide at the center.

Standard Normal Distribution

A standardized version of the normal distribution having a mean of $\mu = 0$ and a standard deviation of $\sigma = 1$.

z-Score

A value indicating how many standard deviations a raw score $x$ is from the mean $\mu$, calculated as $z = \frac{x - \mu}{\sigma}$.

z-Table

A statistical standard normal table providing the proportion of area or probability below a given $z$-score under the standard normal curve.