Individuals

An individual is one object described by a dataset: a person, animal, item, transaction, or time period. Rows usually represent individuals. A medical dataset may assign one row per patient; a sales dataset may assign one per transaction or customer.

Variables

Variables record the characteristics measured or observed for each individual. Columns usually represent variables. The two broad types are quantitative and qualitative, or categorical.

A quantitative variable records a numerical measurement such as height, age, or income. A categorical variable records a label such as gender, nationality, or brand preference.

Categorical Variables

Categorical variables sort observations into discrete labels or groups. Blood type, color preference, and marital status are categorical because each value names a category rather than measuring an amount.

Categorical variables split into two useful classes:

• Nominal variables have no intrinsic order. Gender and country of origin are nominal.
• Ordinal variables have an explicit order. Education level and customer-satisfaction ratings are ordinal.

Pictographs

A pictograph uses icons to encode counts; each icon represents a fixed number of units. It favors immediate recognition over analytical detail, which suits introductory material and public communication.

That simplicity costs precision. Do not use pictographs for detailed technical analysis.

Bar Graphs

Bar graphs compare counts, frequencies, means, or other measures across discrete categories. Bar length encodes the value. Use vertical or horizontal bars according to the labels and available space.

Pie Charts

Pie charts divide a circle into categories whose areas represent proportions of a whole. They work only when the categories exhaust that whole; similar-sized slices are difficult to compare precisely.

Central Tendency

Central tendency compresses a distribution into one representative value:

• Mean: the sum of all values divided by the number of values.
• Median: the middle ordered value, or the mean of the two middle values when the count is even.
• Mode: the most frequent value.

Choose the measure to match the distribution. The median resists skew and outliers; the mean describes symmetric distributions well.

Pie Graphs

A pie graph, pie chart, or circle graph shows categories as percentages of a 100% total. Use it only for genuine parts of one whole.

Two-Way Tables

Two-way tables, or contingency tables, cross-tabulate two categorical variables. One variable runs along each axis so the cells expose their joint counts.

Two-Way Frequency Tables

Two-way relative-frequency tables replace joint counts with proportions or percentages.

• Purpose: Compare category frequencies across groups.
• Example: A table of students by gender and grade level can show each gender's percentage within each grade, or each grade's percentage within each gender.

Use these tables to spot patterns and form hypotheses about relationships between categorical variables.

Venn Diagrams

Venn diagrams use overlapping regions to show relationships among sets. Each overlap contains elements shared by those sets.

• Usefulness: They make similarities and differences visible in probability, logic, statistics, and set theory.