Math 183 Part 2 (Descriptive Statistics and Plots)

Nominal variable

A categorical variable with no natural order (e.g., gender, region, waterfront).

Ordinal variable

A categorical variable with a meaningful order or ranking (e.g., grade, condition, view, yr built, date).

Discrete numerical variable

A numerical variable that takes only specific, separate values (e.g., number of bedrooms, number of bathrooms, number of floors).

Continuous numerical variable

A numerical variable that can take any value within an interval (e.g., price, square footage, latitude, longitude).

Bar plot

A graph used to display the counts or proportions of categories for a categorical or discrete variable.

Pie chart

A circular chart divided into sectors, each sector shows the proportion of each category.

Side-by-side bar plot

A bar plot comparing the distribution of a categorical variable across groups.

Segmented bar plot

A bar plot where each bar is divided into colored segments to show subcategories within the main categories.

Contingency table

A table showing the relationship between two categorical variables.

Histogram

A plot of the frequency or proportion of data falling into each of several bins for a numerical variable.

Binning

Grouping continuous or discrete numerical values into intervals for summarization (e.g., bin years by decade).

Strip chart

A plot where each data point is shown as a small mark along a line, good for visualizing outliers and spread.

Box plot

A plot showing the median, quartiles, range, and potential outliers of a numerical variable.

Mean

The arithmetic average of a numerical dataset.

Median

The middle value in a numerical dataset when ordered.

Quantile

A value that divides the data into equal-sized intervals (e.g., quartiles, percentiles).

Interquartile Range (IQR)

The difference between the 75th and 25th percentiles; describes the spread of the central 50% of data.

Range

The difference between the maximum and minimum values in a dataset.

Variance

A measure of how far data values are from the mean, on average.

Standard deviation

The square root of variance; measures typical distance from the mean.

Robust statistic

A statistic (like median or IQR) that is not heavily affected by outliers.

Skewness

A measure of the asymmetry of a distribution (right-skew = longer right tail, left-skew = longer left tail).

Outlier

A data point much higher or lower than the rest; can affect mean and standard deviation.

Transformation

Applying a function (like log) to a variable to reduce skewness or change its scale.

Scatterplot

A plot that displays the relationship between two numerical variables using points.

Covariance

A measure of how two variables change together (positive: increase together, negative: one up, other down).

Correlation

A standardized measure of linear association between two variables, ranges from -1 to 1.

Simultaneous comparison

Comparing distributions or statistics (like mean or median) across different groups.

Side-by-side boxplot

A plot for comparing the distributions of a numerical variable across groups.

Motivation for inference

Statistical analysis helps determine if observed differences (e.g., between groups) are likely to be real or just due to chance.