Stats chapters 1-5

Statistics

The science of collecting, organizing, and interpreting data.

Individuals

The objects on which data are collected (e.g., students, states, hospitals).

Variables

Characteristics recorded about individuals.

Quantitative Variables

Numeric values with meaningful operations (e.g., height, weight).

Categorical Variables

Groups or categories (e.g., gender, college type).

Identifier Variables

Unique values assigned to individuals (e.g., ID numbers).

Bar Charts

Visual representations of categorical data.

Histograms

Display quantitative data distributions.

Boxplots

Compare distributions and identify outliers.

Mean (x̄)

Sum of all values divided by the number of values.

Median (m)

The middle value when data is ordered.

Range

Difference between the largest and smallest values.

Interquartile Range (IQR)

The difference between Q3 (75th percentile) and Q1 (25th percentile).

Standard Deviation (S)

Measures variation around the mean.

Z-Score

Measures how far a value is from the mean in standard deviations.

68-95-99.7 Rule

Describes Normal Distribution percentages.

Explanatory Variable

The variable suspected to influence another.

Response Variable

The variable that is measured as an outcome.

Simpson’s Paradox

When a relationship between two variables reverses due to a lurking variable.

Proportion

A fraction representing part of a whole (e.g., 0.25 or 1/4).

Percent

A proportion multiplied by 100 (e.g., 0.25 = 25%).

Nominal Variables

Categories without a meaningful order (e.g., colors, names).

Ordinal Variables

Categories with a meaningful order but no consistent difference (e.g., ranking, education level).

Natural Variables

Ordered with meaningful differences (e.g., temperature, income).

Symmetric Distribution

Bell-shaped curve where mean ≈ median.

Right-skewed Distribution

Mean > median.

Left-skewed Distribution

Mean < median.

Bimodal Distribution

Distribution with two peaks.

Standardizing (Z-score)

Tells how many standard deviations a value is from the mean.

Shifting

Adding/subtracting a constant affects mean but not spread.

Scaling

Multiplying/dividing a constant affects both center and spread.

Correlation (R-Value)

Measures the strength of a linear relationship between two quantitative variables.