Average in the context of "Weighted mean"

The national average salary (or national average wage) is the mean salary for the working population of a nation. It is calculated by summing all the annual salaries of all persons in work (surveyed) and dividing the total by the number of workers (surveyed). It is not the same as the Gross domestic product (GDP) per capita, which is calculated by dividing the GDP by the total population of a country, including the unemployed and those not in the workforce (e.g. retired people, children, students, etc.). It can be useful in understanding economic conditions, and to employers and employees in negotiating salaries. The national median salary is usually significantly less than the national average salary because the distribution of workers by salary is skewed.

The median income is the income amount that divides a population into two groups, half having an income above that amount, and half having an income below that amount. It may differ from the mean (or average) income. Both of these are ways of understanding income distribution. Median income can be calculated by household income, by personal income, or for specific demographic groups. When taxes and mandatory contributions are subtracted from income, the result is called net or disposable income. The measurement of income from individuals and households, which is necessary to produce statistics such as the median, can pose challenges and yield results inconsistent with aggregate national accounts data. For example, an academic study on the Census income data claims that when correcting for underreporting, U.S. median gross household income was 15% higher in 2010 (table 3).

A price index (plural: "price indices" or "price indexes") is a normalized average (typically a weighted average) of price relatives for a given class of goods or services in a specific region over a defined time period. It is a statistic designed to measure how these price relatives, as a whole, differ between time periods or geographical locations, often expressed relative to a base period set at 100.

Price indices serve multiple purposes. Broad indices, like the Consumer price index, reflect the economy’s general price level or cost of living, while narrower ones, such as the Producer price index, assist producers with pricing and business planning. They can also guide investment decisions by tracking price trends.  

In mathematics and statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk/ arr-ith-MET-ik), arithmetic average, or just the mean or average is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric and harmonic.

Arithmetic means are also frequently used in economics, anthropology, history, and almost every other academic field to some extent. For example, per capita income is the arithmetic average of the income of a nation's population.

A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and analysing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics) by its aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory, and are frequently nonparametric statistics. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example, in papers reporting on human subjects, typically a table is included giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment or exposure group), and demographic or clinical characteristics such as the average age, the proportion of subjects of each sex, the proportion of subjects with related co-morbidities, etc.

Some measures that are commonly used to describe a data set are measures of central tendency and measures of variability or dispersion. Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness.

In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.

A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.

The Mohorovičić discontinuity (/ˌmoʊhəˈroʊvɪtʃɪtʃ/ MOH-hə-ROH-vih-chitch; Croatian: [moxorôʋiːtʃitɕ]) – usually called the Moho discontinuity, Moho boundary, or just Moho – is the boundary between the crust and the mantle of Earth. It is defined by the distinct change in velocity of seismic waves as they pass through changing densities of rock.

The Moho lies almost entirely within the lithosphere (the hard outer layer of the Earth, including the crust). Only beneath mid-ocean ridges does it define the lithosphere–asthenosphere boundary (the depth at which the mantle becomes significantly ductile). The Mohorovičić discontinuity is 5 to 10 kilometres (3–6 mi) below the ocean floor, and 20 to 90 kilometres (10–60 mi) beneath typical continental crusts, with an average of 35 kilometres (22 mi).

The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables.

The sample mean is the average value (or mean value) of a sample of numbers taken from a larger population of numbers, where "population" indicates not number of people but the entirety of relevant data, whether collected or not. A sample of 40 companies' sales from the Fortune 500 might be used for convenience instead of looking at the population, all 500 companies' sales. The sample mean is used as an estimator for the population mean, the average value in the entire population, where the estimate is more likely to be close to the population mean if the sample is large and representative. The reliability of the sample mean is estimated using the standard error, which in turn is calculated using the variance of the sample. If the sample is random, the standard error falls with the size of the sample and the sample mean's distribution approaches the normal distribution as the sample size increases.