Stats Vocab

Statistics

The science and art of collecting, analyzing, and drawing conclusions from data.

Individual

An object or person described in a set of data (can be people, animals, or things).

Variable

Any attribute or characteristic that takes different values for different individuals.

Categorical Variable

A variable that places an individual into one of several groups or categories.

Quantitative Variable

A variable that takes numerical values for which it makes sense to find an average.

Discrete Variable

A quantitative variable that takes a fixed set of possible values with gaps between them (usually countable).

Continuous Variable

A quantitative variable that can take any numerical value in a given interval (measurable).

Distribution

Tells what values a variable takes and how often it takes those values.

Frequency Table

A table that displays the count (frequency) of individuals in each category or class.

Relative Frequency Table

A table that displays the proportion or percentage of individuals in each category or class.

Bar Chart (Bar Graph)

A graphical display where each category is represented by a bar whose height corresponds to the category's frequency or relative frequency.

Pie Chart

A circular graph that shows how a whole is divided into parts, where the area of each slice is proportional to the percentage of each category.

Two-Way Table

A table that summarizes data on the relationship between two categorical variables for a set of individuals.

Marginal Relative Frequency (Marginal Distribution)

The proportion or percentage of individuals that have a specific value for one categorical variable, located in the margins (row/column totals).

Joint Relative Frequency

The proportion or percentage of individuals that fall into a specific category for both variables simultaneously (located in the inner cells).

Conditional Relative Frequency (Conditional Distribution)

The proportion or percentage of individuals that have a specific value for one variable among individuals who share a specific value of another variable.

Side-by-Side Bar Graph

A graph that displays the distribution of a categorical variable for each category of another variable by placing bars adjacent to each other.

Segmented Bar Graph

A bar graph where each bar represents 100% of a group, divided into colored segments showing the relative proportions of another variable.

Mosaic Plot

A modified segmented bar graph where the width of each bar is proportional to the total number of individuals in that category.

Association

A relationship between two variables where knowing the value of one variable helps predict the value of the other.

Dotplot

A simple graph where each data value is shown as a dot positioned along a horizontal number line.

Symmetric Distribution

A distribution where the right side of the graph (larger half of observations) is approximately a mirror image of the left side.

Skewed Right Distribution

A distribution where the right tail (larger values) is noticeably longer than the left tail.

Skewed Left Distribution

A distribution where the left tail (smaller values) is noticeably longer than the right tail.

Unimodal

A distribution shape characterized by a single prominent peak.

Bimodal

A distribution shape characterized by two distinct, prominent peaks.

Multimodal

A distribution shape characterized by more than two prominent peaks.

Uniform Distribution

A distribution where data values are spread roughly evenly across the entire range with no distinct peak.

Stemplot (Stem-and-Leaf Plot)

A display of quantitative data where each value is split into a 'stem' (all leading digits) and a 'leaf' (the final digit).

Splitting Stems

A method of creating a more detailed stemplot by using multiple stems for the same leading digit (e.g., leaves 0–4 on one stem, 5–9 on the next).

Back-to-Back Stemplot

A stemplot comparing two groups of quantitative data using a common set of stems in the center.

Histogram

A graph that shows quantitative data grouped into adjacent, non-overlapping intervals (bins), with bar heights representing frequency or relative frequency.

Mean (\bar{x})

The arithmetic average of a data set, calculated by summing all values and dividing by the total count: \bar{x} = \frac{\sum x}{n}.

Median (M)

The physical middle value of an ordered distribution such that about 50% of the observations are smaller and 50% are larger.

Range

A single number measuring total spread, calculated as: \text{Range} = \text{Maximum} - \text{Minimum}.

First Quartile (Q_1)

The 25th percentile; the median of the lower half of the data (below the overall median).

Third Quartile (Q_3)

The 75th percentile; the median of the upper half of the data (above the overall median).

Interquartile Range (IQR)

The distance spanning the middle 50% of the data: \text{IQR} = Q_3 - Q_1.

Resistant Measure

A statistical summary (like median and IQR) that is not substantially affected by extreme values or outliers.

Non-Resistant Measure

A statistical summary (like mean, range, and standard deviation) that is sensitive to extreme values and outliers.

Standard Deviation (s_x)

A measure of variability representing the typical distance that data values fall from the mean.

Variance (s_x^2)

The average squared distance of data values from their mean.

Five-Number Summary

A descriptive summary of a quantitative distribution consisting of the Minimum, Q_1, Median, Q_3, and Maximum.

Boxplot

A visual display of the five-number summary featuring a box from Q_1 to Q_3, a line at the median, and whiskers extending to the smallest and largest non-outlier values.

1.5 \times \text{IQR} Outlier Rule

A criterion classifying any observation as an outlier if it falls below Q_1 - 1.5(\text{IQR}) or above Q_3 + 1.5(\text{IQR}).

Percentile

The percentage of observations in a distribution that are less than or equal to a specific value.

Standardized Score (z-score)

The number of standard deviations a value x lies above or below the mean: z = \frac{x - \text{mean}}{\text{standard deviation}}.