Key Concepts
Interval Notation
Inequality | Interval Notation |
[latex]a[latex](a,b)[/latex] |
|
[latex]x>a[/latex] | [latex](a,∞)[/latex] |
[latex]x | [latex](−∞,b)[/latex] |
[latex]x≥a[/latex] | [latex][a,∞)[/latex] |
[latex]x≤b[/latex] | [latex](−∞,b][/latex] |
[latex]a≤x | [latex][a,b)[/latex] |
[latex]a[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
Candela Citations
CC licensed content, Original
- Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution
CC licensed content, Shared previously
- College Algebra. Authored by: Jay Abramson, et al. Lumen Learning. Located at: https://courses.lumenlearning.com/wm-developmentalemporium/chapter/read-describe-solutions-to-inequalities-2/. License: CC BY: Attribution
- Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. Provided by: Monterey Institute of Technology and Education. Located at: http://nrocnetwork.org/dm-opentext. License: CC BY: Attribution
- Concepts in Statistics. Provided by: Open Learning Initiative. Located at: http://oli.cmu.edu. License: CC BY: Attribution