Statistics Midterm Study Guide

Statistics

A way to get information from data.

Population (Pop)

All individuals/items of interest.

Sample

A portion of the population used for analysis.

Descriptive Statistics

Summarizes data (small circle).

Inferential Statistics

Makes predictions based on data (big circle).

Qualitative (Categorical)

Data that can be categorized.

Nominal

No order (e.g., male/female).

Ordinal

Order matters (e.g., ratings: A, B, C).

Quantitative (Numerical)

Data that is measurable.

Discrete

Countable (e.g., children in a household).

Continuous

Measurable (e.g., time, temperature).

Frequency Table

Shows counts and percentages.

Joint Distribution

Combines two variables.

Marginal Distribution

Totals for each variable.

Conditional Distribution

Joint / Marginal.

Histogram

Bars, no gaps. Use ≤ 20 bins.

Mean (Average)

$\bar{x} = \frac{\sum x_i}{n}$.

Median

Middle value (use if skewed).

Mode

Most frequent.

Range

Max - Min.

Interquartile Range (IQR)

$Q_3 - Q_1$.

Percentile

p% are below, (1 - p)% above.

Variance & Standard Deviation

Population: $\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$; Sample: $s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$.

Cross-sectional

Snapshot in time (Microeconomics).

Time-series

Over time (Macroeconomics).

Pooled Cross-sectional

Different people over years.

Panel Data

Same people over years.

Simple Random Sampling (SRS)

Every member has equal chance.

Systematic Sampling

Every kth item after random start.

Stratified Sampling

Split population by characteristics, sample each.

Cluster Sampling

Random clusters sampled (e.g., school districts).

Sampling Frame

List used to choose sample.

Sampling Error

Natural sample-to-sample variation.

Double-Blind Experiment

Neither participant nor researcher knows treatment.

Matching

Pair similar individuals in different groups (hard to implement).

Randomization

Assign randomly to reduce bias.