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 (): The arithmetic average of a data set, calculated by summing all values and dividing by the total count: .
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: .
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: .
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.
Outlier Rule: A criterion classifying any observation as an outlier if it falls below or above .
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: .