Mean in the context of "Arithmetic mean"

In statistics, a confidence interval (CI) is a range of values used to estimate an unknown statistical parameter, such as a population mean. Rather than reporting a single point estimate (e.g. "the average screen time is 3 hours per day"), a confidence interval provides a range, such as 2 to 4 hours, along with a specified confidence level, typically 95%.

A 95% confidence level does not imply a 95% probability that the true parameter lies within a particular calculated interval. The confidence level instead reflects the long-run reliability of the method used to generate the interval. In other words, if the same sampling procedure were repeated 100 times from the same population, approximately 95 of the resulting intervals would be expected to contain the true population mean.

Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datum – a standardised geodetic datum – that is used, for example, as a chart datum in cartography and marine navigation, or, in aviation, as the standard sea level at which atmospheric pressure is measured to calibrate altitude and, consequently, aircraft flight levels. A common and relatively straightforward mean sea-level standard is instead a long-term average of tide gauge readings at a particular reference location.

The term above sea level generally refers to the height above mean sea level (AMSL). The term APSL means above present sea level, comparing sea levels in the past with the level today.

In statistics, as opposed to its general use in mathematics, a parameter is any quantity of a statistical population that summarizes or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which provide a comprehensive description of the population and can be considered to define a probability distribution for the purposes of extracting samples from this population.

A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean, which is the mean of gathered data per sampling, called sample). Thus a "statistical parameter" can be more specifically referred to as a population parameter.

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).

This is a list of countries of the world by wealth per adult, from UBS's Global Wealth Databook. Wealth includes both financial and non-financial assets.

UBS publishes various statistics relevant for calculating net wealth. These figures are influenced by real estate prices, equity market prices, exchange rates, liabilities, debts, adult percentage of the population, human resources, natural resources and capital and technological advancements, which may create new assets or render others worthless in the future.

In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is$${\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}\,.}$$

The parameter ⁠${\displaystyle \mu }$⁠ is the mean or expectation of the distribution (and also its median and mode), while the parameter ${\textstyle \sigma ^{2}}$ is the variance. The standard deviation of the distribution is ⁠${\displaystyle \sigma }$⁠ (sigma). A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.

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 statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, variance is the average of the squared deviations from the mean.) A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. Standard deviation can also be used to calculate standard error for a finite sample, and to determine statistical significance.