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
