UNIT 1 STATS PLUS

Statistics

Science of data that turns data into knowledge.

Population

Entire group being studied.

Sample

Small group from the population.

Variable

The characteristic being measured.

Quantitative Data

Numerical data such as height, weight, and test scores.

Qualitative Data

Categorical data such as gender, colors, and brands.

Parameter

Data from a population.

Statistic

Data from a sample.

Simple Random Sample (SRS)

Everyone has an equal chance of being selected.

Stratified Sample

Divide into groups and sample some from each.

Cluster Sample

Divide into groups and sample entire groups.

Systematic Sample

Select every nth person from a list.

Anecdote

Personal story that is considered unreliable.

Observational Study

No interference, only observes associations.

Controlled Experiment

Researcher assigns treatments and determines causality.

Good Experiment Feature: Sample Size

Should be at least 30 for reliability.

Good Experiment Feature: Random Assignment

Reduces bias.

Good Experiment Feature: Blinding

Hides treatment to prevent bias.

Good Experiment Feature: Placebo

Fake treatment used for comparison.

Two-Way Tables

Used to compare two variables.

Percentage Calculation Formula

Part/Total × 100%.

Dotplot

Each data point is represented as a dot.

Histogram

Data grouped into intervals and represented by bars.

Stemplot

Breaks data into stems and leaves for representation.

Describe Distributions: Shape

Can be symmetric or skewed.

Describe Distributions: Center

Middle value (mean or median).

Describe Distributions: Spread

Refers to how spread out the data is.

Bar Graph

Separate bars for each category in categorical data.

Pie Chart

Shows percentage of each category.

Mean (x̄)

Calculated as sum of data divided by number of values.

Median

Middle value of a dataset after sorting.

Mode

Most frequent value in a dataset.

Range

Difference between the highest and lowest value.

Standard Deviation (σ or s)

Average difference from the mean.

Empirical Rule (68-95-99.7 Rule)

In symmetric distributions, 68% of data is within 1 standard deviation, 95% within 2, and 99.7% within 3.