A Population and Sample Statistics

A random variable is defined as a variable that can assume any value from a set of possible values. A statistic or statistical parameter is any quantity computed from a sample it is characteristic of the sample, and it is used to estimate the characteristics of the population variable. 

Degrees of freedom can be defined as the number of observations made in excess of the minimum theoretically necessary to estimate a statistical parameter or any unknown quantity. 

Let us use the notation N to designate the total number of items in the population under study, where 0 s iV and n to specify the number of items contained in the sample taken from that population, where 0 s n N. The variable being investigated will be designated as X it may have discrete values, or it may be a continuous function, in the range - jr =. For specific populations, these ranges may be more limited, as will be mentioned below. 

For the sake of example and in order to clarify these terms, let us consider for study the entire human population and examine the age of this population. The value of A, in this case, would be approximately 6 billion. The age variable would range from 0 to possibly 150 years. Age can be considered either as a continuous variable, because all ages are possible, or more commonly as a discrete variable, because ages are usually grouped by year. In the continuous case, the age variable takes an infinite number of values in the range 0 x 150, and in the 

Assume that a random sample of n persons is chosen from the total population (say n = 1 million) and the age of each person in the sample is recorded. 

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