# Population Mean Value

A Population Mean Value is a population parameter that is a central tendency measure, the mean value, of a population.

## References

### 2017

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Mean
• For a data set, the terms arithmetic mean, mathematical expectation, and sometimes average are used synonymously to refer to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted by $\displaystyle{ \bar{x} }$, pronounced "x bar". If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is termed the sample mean (denoted $\displaystyle{ \bar{x} }$) to distinguish it from the population mean (denoted $\displaystyle{ \mu }$ or $\displaystyle{ \mu_x }$).[1]

For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population. For example, the population mean height is equal to the sum of the heights of every individual divided by the total number of individuals. The sample mean may differ from the population mean, especially for small samples. The law of large numbers dictates that the larger the size of the sample, the more likely it is that the sample mean will be close to the population mean.[2]

### 1996

1. Underhill, L.G.; Bradfield d. (1998) Introstat, Juta and Company Ltd. ISBN 0-7021-3838-X p. 181
2. Schaum's Outline of Theory and Problems of Probability by Seymour Lipschutz and Marc Lipson, p. 141