Half Mode
- Identifies the single most likely outcome in a probability distribution.
- Applied in contexts where outcome probabilities are not equally likely.
- Distinct from the average or expected value, which account for all outcomes and their probabilities.
Definition
Section titled “Definition”Half-mode is a concept in probability that refers to the most likely value or outcome of a random event — i.e., the value that has the highest probability of occurring in a given situation. It is presented as a variation of the mode concept used in situations where the probabilities of the possible outcomes are not equally likely.
Explanation
Section titled “Explanation”The mode of a probability distribution is the value with the highest probability of occurring. Half-mode uses this notion to identify the single most likely outcome when outcome probabilities differ. According to the source content, half-mode is employed in cases where the mode of the distribution is said to be not well-defined, so the half-mode concept is used instead. Half-mode focuses only on the most likely outcome and does not account for the probabilities of all outcomes the way the average or expected value does.
Examples
Section titled “Examples”Example 1 — Biased coin
Section titled “Example 1 — Biased coin”Suppose we have a coin that has a 60% probability of landing on heads and a 40% probability of landing on tails when flipped. In this case, the half-mode of the distribution would be heads, since it is the most likely outcome.
Example 2 — Fair six-sided die
Section titled “Example 2 — Fair six-sided die”Suppose we have a dice that has a 20% probability of landing on each of the numbers 1, 2, 3, 4, 5, and 6 when rolled. In this case, the half-mode of the distribution would be any of the numbers 1, 2, 3, 4, 5, or 6, since all of these numbers have an equal probability of occurring.
Related terms
Section titled “Related terms”- Mode
- Average
- Expected value