Confidence interval in the context of Confidence region

In world demographics, the world population is the total number of humans currently alive. It was estimated by the United Nations to have exceeded eight billion in mid-November 2022. It took around 300,000 years of human prehistory and history for the human population to reach a billion and only 218 more years from there to reach 8 billion.

The human population has experienced continuous growth following the Great Famine of 1315–1317 and the end of the Black Death in 1350, when it was nearly 370,000,000. The highest global population growth rates, with increases of over 1.8% per year, occurred between 1955 and 1975, peaking at 2.1% between 1965 and 1970. The growth rate declined to 1.1% between 2015 and 2020 and is projected to decline further in the 21st century. The global population is still increasing, but there is significant uncertainty about its long-term trajectory due to changing fertility and mortality rates. The UN Department of Economics and Social Affairs projects between 9 and 10 billion people by 2050 and gives an 80% confidence interval of 10–12 billion by the end of the 21st century, with a growth rate by then of zero. Other demographers predict that the human population will begin to decline in the second half of the 21st century.

The chronology of the universe describes the history and future of the universe according to Big Bang cosmology.

Research published in 2015 estimates the earliest stages of the universe's existence as taking place 13.8 billion years ago, with an uncertainty of around 21 million years at the 68% confidence level.

This article lists current estimates of the world population in history. In summary, estimates for the progression of world population since the Late Middle Ages are in the following ranges:

Estimates for pre-modern times are necessarily fraught with great uncertainties, and few of the published estimates have confidence intervals; in the absence of a straightforward means to assess the error of such estimates, a rough idea of expert consensus can be gained by comparing the values given in independent publications. Population estimates cannot be considered accurate to more than two decimal digits; for example, the world population for the year 2012 was estimated at 7.02, 7.06, and 7.08 billion by the United States Census Bureau, the Population Reference Bureau, and the United Nations Department of Economic and Social Affairs, respectively, corresponding to a spread of estimates of the order of 0.8%.

The Challenger Deep is the deepest known point of the seabed of Earth, located in the western Pacific Ocean at the southern end of the Mariana Trench, in the ocean territory of the Federated States of Micronesia.

The GEBCO Gazetteer of Undersea Feature Names indicates that the feature is situated at 11°22.4′N 142°35.5′E / 11.3733°N 142.5917°E / 11.3733; 142.5917 and has an approximated maximum depth of 10,903 to 11,009 m (35,771 to 36,119 ft) below sea level. A 2011 study placed the depth at 10,920 ± 10 m (35,827 ± 33 ft) with a 2021 study revising the value to 10,935 ± 6 m (35,876 ± 20 ft) at a 95% confidence level.

Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter". The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information. An estimate that turns out to be incorrect will be an overestimate if the estimate exceeds the actual result and an underestimate if the estimate falls short of the actual result.

The confidence in an estimate is quantified as a confidence interval, the likelihood that the estimate is in a certain range. Human estimators systematically suffer from overconfidence, believing that their estimates are more accurate than they actually are.

The plus–minus sign or plus-or-minus sign (±) and the complementary minus-or-plus sign (∓) are symbols with broadly similar multiple meanings.

• In mathematics, the ± sign generally indicates a choice of exactly two possible values, one of which is obtained through addition and the other through subtraction. The ∓ is typically used only in tandem with the ± sign and indicates that in the case that the ± is a +, the ∓ would be a − (and vice-versa).
• In statistics and experimental sciences, the ± sign commonly indicates the confidence interval or uncertainty bounding a range of possible errors in a measurement, often the standard deviation or standard error. The sign may also represent an inclusive range of values that a reading might have.
• In chess, the ± sign indicates a clear advantage for the white player; the complementary minus-plus sign (∓) indicates a clear advantage for the black player.

Other meanings occur in other fields, including medicine, engineering, chemistry, electronics, linguistics, and philosophy.

In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate.

Point estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequentist inference, or credible intervals, in the case of Bayesian inference. More generally, a point estimator can be contrasted with a set estimator. Examples are given by confidence sets or credible sets. A point estimator can also be contrasted with a distribution estimator. Examples are given by confidence distributions, randomized estimators, and Bayesian posteriors.

In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, ${\displaystyle P=\Sigma ^{-1}}$.For univariate distributions, the precision matrix degenerates into a scalar precision, defined as the reciprocal of the variance, ${\displaystyle p={\frac {1}{\sigma ^{2}}}}$.

Other summary statistics of statistical dispersion also called precision (or imprecision)include the reciprocal of the standard deviation, ${\displaystyle p={\frac {1}{\sigma }}}$; the standard deviation itself and the relative standard deviation;as well as the standard error and the confidence interval (or its half-width, the margin of error).

The standard error (SE) of a statistic (usually an estimator of a parameter, like the average or mean) is the standard deviation of its sampling distribution. The standard error is often used in calculations of confidence intervals.

The sampling distribution of a mean is generated by repeated sampling from the same population and recording the sample mean per sample. This forms a distribution of different sample means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean.

The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a simultaneous census of the entire population. The margin of error will be positive whenever a population is incompletely sampled and the outcome measure has positive variance, which is to say, whenever the measure varies.

The term margin of error is often used in non-survey contexts to indicate observational error in reporting measured quantities.