1. What is Statistics?

Statistics: The science of collecting, organizing, analyzing, interpreting, and presenting data to help make informed decisions based on evidence.

Two Branches of Statistics

Descriptive Statistics

Purpose: Summarize and describe data you've already collected

What it does: Uses numbers, graphs, and tables to paint a picture of your data

Example: "The average test score in our class was 82%"

Think of it as: "What happened?"

Inferential Statistics

Purpose: Make predictions or generalizations about a larger population based on a sample

What it does: Uses probability and mathematical techniques to draw conclusions beyond your data

Example: "Based on polling 1,000 voters, we predict 52% of all voters will support Candidate A"

Think of it as: "What can we conclude or predict?"

CRITICAL CONCEPT: Correlation ≠ Causation
Just because two things are related doesn't mean one causes the other!

2. Types of Data

Main Categories

Quantitative (Numerical)	Qualitative (Categorical)
Data measured with numbers Can do math operations	Data that describes characteristics Categories/labels
Examples: Height, age, weight, temperature, test scores	Examples: Eye color, gender, major, zip code, car type

Quantitative Data Subtypes

Discrete	Continuous
Only specific values (usually whole numbers) You count it	Any value in a range (including decimals) You measure it
Examples: Number of students (25, 26, 27), dice rolls, cars in lot	Examples: Height (5'8.2"), weight (150.3 lbs), temperature (72.5°F)

Levels of Measurement

Level	Description	Examples
Nominal	Categories with no order	Eye color, zip codes, student ID
Ordinal	Categories with meaningful order, but unequal gaps	Class rank (1st, 2nd, 3rd), satisfaction (low, medium, high)
Interval	Equal intervals, NO true zero	Temperature (°F, °C), IQ scores, calendar years
Ratio	Equal intervals + true zero	Height, weight, age, income (zero = none)

3. Data Collection Methods

Three Main Methods

Method	Description	Can Establish Causation?
Observational Study	Observe without interfering	No - only association
Survey	Ask people questions	No - only association
Experiment	Manipulate variables with random assignment	YES - can show causation!

Only EXPERIMENTS with random assignment can establish cause-and-effect relationships!

Sampling Methods

Method	Description	Quality
Simple Random	Every member has equal chance of selection	Good
Stratified	Divide into groups, randomly sample from each	Good
Cluster	Randomly select entire groups	Good
Systematic	Select every kth member	Usually good
Convenience	Sample whoever is easy to reach	BIASED
Voluntary Response	People self-select to participate	VERY BIASED

Key Terms

Population: The entire group you want to study

Sample: A subset of the population that you actually collect data from

Parameter: A numerical summary of the population (usually unknown)

Statistic: A numerical summary of the sample (what we calculate)

4. Data Visualization

Choosing the Right Graph

Graph Type	Data Type	Purpose
Bar Chart	Categorical	Compare categories (bars have gaps)
Histogram	Continuous numerical	Show distribution (bars touch!)
Pie Chart	Categorical (percentages)	Show parts of whole (adds to 100%)
Line Graph	Time series	Show trends over time
Scatterplot	Two quantitative variables	Show relationship between variables

Bar Chart vs. Histogram:
• Bar charts: Bars have GAPS (categorical data)
• Histograms: Bars TOUCH (continuous data)

Misleading Graph Techniques (Watch Out!)

Truncated Y-Axis: Starting bar chart above zero exaggerates differences
Cherry-Picking Time Periods: Showing only part of data to tell specific story
3D Effects: Distorting proportions with unnecessary visual effects
Inappropriate Graph Type: Using wrong graph makes comparisons impossible
Dual Y-Axes Manipulation: Scaling axes to create false correlations

Best Practices

Start bar charts at zero
Label everything clearly (axes, units, title, legend)
Use appropriate graph type for your data
Keep it simple - avoid unnecessary decorations
Show full context - don't cherry-pick
Include data source and sample size

Quick Reference: Key Formulas & Concepts

Mean (Average)

Mean = (Sum of all values) ÷ (Number of values)

Important Reminders

1. Correlation ≠ Causation
2. Only experiments can establish causation
3. Convenience and voluntary response samples are biased
4. Bar chart bars have gaps; histogram bars touch
5. Always question: "How was this data collected?"

Module 1: Introduction to Statistics & Data

Free Statistics Learning Platform • safaa dabagh • sdabagh.github.io

Module 1 Study Guide