Difference between revisions of "Mean"
m (→Types of Means) |
|||
| (5 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
| − | The '''mean''' of a set of real numbers usually refers to the [[arithmetic mean]] of the set (also known as the [[average]]). | + | The '''mean''' of a set of real numbers usually refers to the [[arithmetic mean]] of the set (also known as the [[average]]). For example, the arithmetic mean of the members of the set {3, 5, 10} is |
| + | <math> \frac{3 + 5 + 10}{3} = \frac{18}{3} = 6. </math> | ||
| + | |||
| + | |||
| + | However, there are numerous other kinds of various means used in [[mathematics]] and [[statistics]]. | ||
| + | |||
| + | |||
| + | ==Mean, Median, Mode== | ||
| + | https://youtu.be/TkZvMa30Juo?t=1504 | ||
== Types of Means == | == Types of Means == | ||
| Line 7: | Line 15: | ||
* [[Harmonic mean]] | * [[Harmonic mean]] | ||
* [[Power mean]] | * [[Power mean]] | ||
| − | * [[ | + | * [[Quadratic mean]] (also known as the root mean square) |
The arithmetic mean, geometric mean, harmonic mean, and root mean square are all special cases of the power mean. | The arithmetic mean, geometric mean, harmonic mean, and root mean square are all special cases of the power mean. | ||
| − | |||
== Inequalities and Optimization == | == Inequalities and Optimization == | ||
There are numerous [[inequality | inequalities]] that relate different types of means. The most common are part of the RMS-AM-GM-HM inequality chain. This inequality chain is a set of special cases of the [[Power mean inequality]]. | There are numerous [[inequality | inequalities]] that relate different types of means. The most common are part of the RMS-AM-GM-HM inequality chain. This inequality chain is a set of special cases of the [[Power mean inequality]]. | ||
| + | |||
| + | == See Also == | ||
| + | |||
| + | * [[Median of a set]] | ||
| + | |||
| + | * [[Mode of a set]] | ||
Latest revision as of 14:28, 12 November 2023
The mean of a set of real numbers usually refers to the arithmetic mean of the set (also known as the average). For example, the arithmetic mean of the members of the set {3, 5, 10} is
However, there are numerous other kinds of various means used in mathematics and statistics.
Mean, Median, Mode
https://youtu.be/TkZvMa30Juo?t=1504
Types of Means
- Arithmetic mean
- Geometric mean
- Harmonic mean
- Power mean
- Quadratic mean (also known as the root mean square)
The arithmetic mean, geometric mean, harmonic mean, and root mean square are all special cases of the power mean.
Inequalities and Optimization
There are numerous inequalities that relate different types of means. The most common are part of the RMS-AM-GM-HM inequality chain. This inequality chain is a set of special cases of the Power mean inequality.
