Summary: Review

Key Concepts

Interval Notation

Inequality Interval Notation
[latex]a<x<b[/latex] [latex](a,b)[/latex]
[latex]x>a[/latex] [latex](a,∞)[/latex]
[latex]x<b[/latex] [latex](−∞,b)[/latex]
[latex]x≥a[/latex] [latex][a,∞)[/latex]
[latex]x≤b[/latex] [latex](−∞,b][/latex]
[latex]a≤x<b[/latex] [latex][a,b)[/latex]
[latex]a<x≤b[/latex] [latex](a,b][/latex]
[latex]a≤x≤b[/latex] [latex][a,b][/latex]

For a finite interval [latex](a,b), (a,b], [a,b) \ \mathrm{or} \ [a,b][/latex].

  • The width is [latex]b-a[/latex]
  • The midpoint is [latex]\frac{a+b}{2}[/latex]

Population and sample mean, variance, and standard deviation

Population  Sample
Population size [latex]N[/latex] Sample size [latex]n[/latex]
Population mean [latex]\mu = \frac{\sum{x}}{N}[/latex] Sample mean [latex]\overline{x}=\frac{\sum{x}}{n}[/latex]
Population variance [latex]\sigma ^2. = \frac{\sum{(x- \mu)^2}}{N}[/latex] Sample variance [latex]s^2=\frac{\sum{(x-\overline{x})^2}}{n-1}[/latex]
Population standard deviation [latex]\sigma = \sqrt{\frac{\sum{(x-\mu)^2}}{N}}[/latex] Sample standard deviation [latex]s=\sqrt{\frac{\sum{(x-\overline{x})^2}}{n-1}}[/latex]

Glossary

  • interval: a set of numbers in which a solution falls
  • population: the entire group of individuals or objects of interest
  • parameter: a numerical characteristic of a population
  • sample: portion, or subset, of a population
  • statistic: a numerical characteristic of a sample