Weighted average is a single number or value that best represents a set of data, when each data point is assigned different "weights" or importance. The most common weighted average is the weighted arithmetic mean, which is similar to an ordinary arithmetic mean except some data points contribute more than others. Other cases include the weighted geometric mean and weighted harmonic mean.
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👉 Weighted average in the context of International Atomic Time
International Atomic Time (abbreviated TAI, from its French name temps atomique international) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 atomic clocks in over 80 national laboratories worldwide. It is a continuous scale of time, without leap seconds, and it is the principal realisation of Terrestrial Time (with a fixed offset of epoch). It is the basis for Coordinated Universal Time (UTC), which is used for civil timekeeping all over the Earth's surface and which has leap seconds.
UTC deviates from TAI by a number of whole seconds. As of 1 January 2017, immediately after the most recent leap second was put into effect, UTC has been exactly 37 seconds behind TAI. The 37 seconds result from the initial difference of 10 seconds at the start of 1972, plus 27 leap seconds in UTC since 1972. In 2022, the General Conference on Weights and Measures decided to abandon the leap second by or before 2035, at which point the difference between TAI and UTC will remain fixed.
In this Dossier
- ⭐ Core Definition: Weighted average
- 👉 Weighted average in the context of International Atomic Time
- Weighted average in the context of Expected value
- Weighted average in the context of Atlas method
- Weighted average in the context of Optimal decision
- Weighted average in the context of OPEC Reference Basket
- Weighted average in the context of Weight function
Weighted average in the context of Expected value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration.
Weighted average in the context of Atlas method
The World Bank has used the Atlas method since 1993 to estimate the economic size of countries based on their gross national income (GNI) in U.S. dollars.
To convert a country's GNI from its local currency to U.S. dollars, the Atlas method uses a conversion factor that averages exchange rates over three years. This helps reduce the impact of temporary exchange rate changes. Additionally, it adjusts for differences in inflation rates between the country (using its GDP deflator) and several developed countries (using a weighted average of their GDP deflators in Special Drawing Rights, or SDR, terms). The converted GNI in U.S. dollars is then divided by the country's midyear population to determine GNI per capita.
Weighted average in the context of Optimal decision
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory. In order to compare the different decision outcomes, one commonly assigns a utility value to each of them.
If there is uncertainty as to what the outcome will be but one has knowledge about the distribution of the uncertainty, then under the von Neumann–Morgenstern axioms the optimal decision maximizes the expected utility (a probability–weighted average of utility over all possible outcomes of a decision). Sometimes, the equivalent problem of minimizing the expected value of loss is considered, where loss is (–1) times utility. Another equivalent problem is minimizing expected regret.
Weighted average in the context of OPEC Reference Basket
The OPEC Reference Basket (ORB), also referred to as the OPEC Basket, is a weighted average of prices for petroleum blends produced by OPEC members. It is used as an important benchmark for crude oil prices. OPEC has often attempted to keep the price of the OPEC Basket between upper and lower limits, by increasing and decreasing production. This makes the measure important for market analysts. The OPEC Basket, including a mix of light and heavy crude oil products, is heavier than both Brent crude oil, and West Texas Intermediate crude oil.
Since January 1, 2017, the OPEC reference basket consists of a weighted average of the following crudes:
Weighted average in the context of Weight function
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be employed in both discrete and continuous settings. They can be used to construct systems of calculus called "weighted calculus" and "meta-calculus".