Arithmetic mean in the context of Velocity dispersion

The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the “middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics.

Median is a 2-quantile; it is the value that partitions a set into two equal parts.

The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light and infrared radiation with 10% at ultraviolet energies. It is the main source of energy for life on Earth. The Sun has been an object of veneration in many cultures and a central subject for astronomical research since antiquity.

The Sun orbits the Galactic Center at a distance of 24,000 to 28,000 light-years. Its mean distance from Earth is about 1.496×10 kilometres or about 8 light-minutes. The distance between the Sun and the Earth was used to define a unit of length called the astronomical unit, now defined to be 149.5978707×10 kilometres. Its diameter is about 1,391,400 km (864,600 mi), 109 times that of Earth. The Sun's mass is about 330,000 times that of Earth, making up about 99.86% of the total mass of the Solar System. The mass of the Sun's surface layer, its photosphere, consists mostly of hydrogen (~73%) and helium (~25%), with much smaller quantities of heavier elements, including oxygen, carbon, neon, and iron.

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.

The arithmetic mean, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x₁, x₂, ..., x_n is typically denoted using an overhead bar, ${\displaystyle {\bar {x}}}$. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the sample mean (${\displaystyle {\bar {x}}}$) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted ${\displaystyle \mu }$ or ${\displaystyle \mu _{x}}$.

Compound annual growth rate (CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of various data values, such as revenue growth of companies, or of economic values, over time.

Greenwich Mean Time (GMT) is the local mean time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a consequence, it cannot be used to specify a particular time unless a context is given. The term "GMT" is also used as one of the names for the time zone UTC+00:00 and, in UK law, is the basis for civil time in the United Kingdom.

Because of Earth's uneven angular velocity in its elliptical orbit and its axial tilt, noon (12:00:00) GMT is rarely the exact moment the Sun crosses the Greenwich Meridian and reaches its highest point in the sky there. This event may occur up to 16 minutes before or after noon GMT, a discrepancy described by the equation of time. Noon GMT is the annual average (the arithmetic mean) moment of this event, which accounts for the word "mean" in "Greenwich Mean Time".

Accuracy and precision are measures of observational error; accuracy is how close a given set of measurements is to the true value and precision is how close the measurements are to each other.

The International Organization for Standardization (ISO) defines a related measure:trueness, "the closeness of agreement between the arithmetic mean of a large number of test results and the true or accepted reference value."

A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function (e.g., a calculation method of the average) and for the value of the function on a given sample (e.g., the result of the average calculation). When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose.

When a statistic is used for estimating a population parameter, the statistic is called an estimator. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the sample mean is an unbiased estimator of the population mean. This means that the expected value of the sample mean equals the true population mean.

An average of a collection or group is a value that is most central or most common in some sense, and represents its overall position.

In mathematics, especially in colloquial usage, it most commonly refers to the arithmetic mean, so the "average" of the list of numbers [2, 3, 4, 7, 9] is generally considered to be (2+3+4+7+9)/5 = 25/5 = 5. In situations where the data is skewed or has outliers, and it is desired to focus on the main part of the group rather than the long tail, "average" often instead refers to the median; for example, the average personal income is usually given as the median income, so that it represents the majority of the population rather than being overly influenced by the much higher incomes of the few rich people. In certain real-world scenarios, such computing the average speed from multiple measurements taken over the same distance, the average used is the harmonic mean. In situations where a histogram or probability density function is being referenced, the "average" could instead refer to the mode. Other statistics that can be used as an average include the mid-range and geometric mean, but they would rarely, if ever, be colloquially referred to as "the average".

The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox.

Raw data, also known as primary data, are data (e.g., numbers, instrument readings, figures, etc.) collected from a source. In the context of examinations, the raw data might be described as a raw score (after test scores).

If a scientist sets up a computerized thermometer which records the temperature of a chemical mixture in a test tube every minute, the list of temperature readings for every minute, as printed out on a spreadsheet or viewed on a computer screen are "raw data". Raw data have not been subjected to processing, "cleaning" by researchers to remove outliers, obvious instrument reading errors or data entry errors, or any analysis (e.g., determining central tendency aspects such as the average or median result). As well, raw data have not been subject to any other manipulation by a software program or a human researcher, analyst or technician. They are also referred to as primary data. Raw data is a relative term (see data), because even once raw data have been "cleaned" and processed by one team of researchers, another team may consider these processed data to be "raw data" for another stage of research. Raw data can be inputted to a computer program or used in manual procedures such as analyzing statistics from a survey. The term "raw data" can refer to the binary data on electronic storage devices, such as hard disk drives (also referred to as "low-level data").

The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule.

For a homopolymer, there is only one type of monomeric unit and the number-average degree of polymerization is given by ${\displaystyle {\overline {DP}}_{n}\equiv {\overline {X}}_{n}={\frac {{\overline {M}}_{n}}{M_{0}}}}$,where ${\displaystyle {\overline {M}}_{n}}$ is the number-average molecular weight and ${\displaystyle M_{0}}$ is the molecular weight of the monomer unit. The overlines indicate arithmetic mean values. For most industrial purposes, degrees of polymerization in the thousands or tens of thousands are desired. This number does not reflect the variation in molecule size of the polymer that typically occurs, it only represents the mean number of monomeric units.

In mathematics, the geometric mean (also known as the mean proportional) is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean, which uses their sum). The geometric mean of ⁠${\displaystyle n}$⁠ numbers is the nth root of their product, i.e., for a collection of numbers a₁, a₂, ..., a_n, the geometric mean is defined as

When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm ⁠${\displaystyle \ln }$⁠ of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function ⁠${\displaystyle \exp }$⁠,

The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean, median, mode, or the result of any other measure of central tendency or any reference value related to the given data set. AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated as MAD).

In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in

• a measure of location, or central tendency, such as the arithmetic mean
• a measure of statistical dispersion like the standard mean absolute deviation
• a measure of the shape of the distribution like skewness or kurtosis
• if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient

A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.