UNIT 1 STATS PLUS

Statistics Basics

• Statistics: Science of data → turns data into knowledge.

• Population: Entire group being studied.

• Sample: Small group from the population.

• Variable: The characteristic being measured.

Types of Data

• Quantitative (Numerical): Numbers (height, weight, test scores).

• Qualitative (Categorical): Groups/categories (gender, colors, brands).

Parameters vs. Statistics

• Parameter: Data from a population.

• Statistic: Data from a sample.

Sampling Methods

1. Simple Random Sample (SRS) – Everyone has an equal chance.

2. Stratified Sample – Divide into groups, sample some from each.

3. Cluster Sample – Divide into groups, sample entire groups.

4. Systematic Sample – Pick every nth person from a list.

Types of Studies

• Anecdote – Personal story (unreliable).

• Observational Study – No interference, only observes associations.

• Controlled Experiment – Researcher assigns treatments (determines causality).

Good Experiment Features

• Large sample size (at least 30).

• Random assignment (reduces bias).

• Blinding (hides treatment to prevent bias).

• Placebo (fake treatment for comparison).

Two-Way Tables

• Compare two variables (e.g., commuters vs. breakfast habits).

• Percentage calculations: part/total × 100%.

Graphs for Numerical Data

• Dotplot – Each data point is a dot.

• Histogram – Data grouped into intervals (bars).

• Stemplot – Breaks data into stems & leaves.

Describe Distributions

• Shape: Symmetric or skewed?

• Center: Middle value (mean or median).

• Spread: How spread out the data is.

Graphs for Categorical Data

• Bar Graph – Separate bars for each category.

• Pie Chart – Shows percentage of each category.

Measures of Center (Averages)

• Mean (x̄) = sum of data ÷ number of values.

• Median = Middle value (after sorting).

• Mode = Most frequent value.

Measures of Dispersion (Spread of Data)

• Range = Highest value - Lowest value.

• Standard Deviation (σ or s) = Average difference from the mean.

Empirical Rule (68-95-99.7 Rule)

• For symmetric (normal) distributions:

  • 68% of data within 1 standard deviation.

  • 95% of data within 2 standard deviations.

  • 99.7% of data within 3 standard deviations.