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A population parameter or an approximate value entering the probability distribution of an abstract statistic is usually described in terms of its normal distribution or mean value. It is often used to describe the range of values that may occur at some desired population level, and is typically derived from a sample statistic or data point or from the distribution of samples or data in a study.

One example of an approximate value used in statistics is the population standard deviation or SD. This is the difference between the average value of the sample and the expected value based on that sample. The higher the SD, the smaller the sample size. If the sample size is small enough and the standard deviation is high enough, then the distribution is highly non-normal, and most likely will have a regular shape. This is because in a normal population the mean of the population distribution is close to its mean value, so the SD is relatively large compared with the mean.

The SD is also often related to the sample size. When the sample size is very small, the SD is high. On the other hand, when the sample size is quite large, the SD is lower. Also, the degree of dispersion of the sample mean and SD is less likely to be significantly different than the normality of the population mean and SD.

Population parameters are a crucial part of any type of population estimation or statistical modeling. Population parameter values often vary depending on the size of the sample design. For example, if the sample size is too large for the population to be statistically meaningful, the value of the parameter will be too high. If the sample size is too small, then the parameter will be too low.

Another way to describe a population parameter is its normal distribution. A normal distribution refers to the set of distributions in which the data in a given population distribution may occur, with each value occurring equally often. In statistics, a normal distribution is often used to describe the distributions of values at a given sample mean.

Population parameter values also differ with time. If there is only one time element or event, then the parameter is called a linear time trend, or autoregressive process. Otherwise, it is called a bimodal or spline time process.

Population distributions are also described as normal if they are approximately normal. when all points are equally likely to occur. If there are two or more time elements, then they are called multimodal. A multimodal distribution is normal if the distributions of the data have a certain frequency or distribution over the range of values expected to occur with the data.

Population distributions can also be described as normal if they have a definite shape. For example, if there is a uniform distribution for all time-varying time points, it is normal, whereas if the distribution varies over a range, it is called a non-uniform distribution. This is usually used to refer to the distribution of values over time or within a range.

Population distributions are also referred to as normal if they are uniform for all values over the range. However, they are not necessarily normal. The distribution of values over a range in the range of the distribution is normal for the values that occur at a point, but is not normal for values that occur at some other points in the range. Also, the distribution over a range of values at points is normal for values that occur at one time, but is not normal for values that occur at a later time.

The distribution over a range is also called normal if it has a definite shape. If it has a definite, negative slope, it is called a steeply peaked distribution, while if it has a definite, positive slope, it is called a concavely peaked distribution. When a distribution has a definite curve, it is referred to as a bell-shaped or a K-curve. If the distribution has no definite curve, it is called a U-curve.

Population distribution can be described as normal if it is symmetrical, that is, if the values occur over all points in the distribution. If it is non-symmetrical, it is said to have a power law distribution. If it is a bimodal distribution, it is said to have a high level of variance over the range of values, although it is not necessarily normal.

Other characteristics of the distribution are called significance. These can include significance distributions (for distributions that are symmetrical), significance distributions that are symmetric but not necessarily the same, significance distributions with a high level of variance, and power distributions (for distributions that are not symmetrical).

Editor-in-Chief since 2011.