004. Basic Definitions

In any statistical study, the researcher is interested in a certain collection or set of observations called the Population (or universe).

Example 1.1. If the chief executive officer (CEO) for a large manufacturing firm wishes to study the output of all plants owned by the firm, then the output of all plants is the population.

A Parameter is a descriptive measure of the entire population of all observations of interest to the researcher. A parameter Describes a population.

Example 1.2. The total output of all the manufacturing plants.

A Sample is a representative portion of the population which is selected for study because the population is too large to examine in its entirely. A sample is a scientifically selected subset of the population. Samples are necessary because studying entire populations is too time-consuming and costly.

Example 1.3. Each month the US Department of Labor calculates the average income of a sample of only several thousand wage earners selected from the entire population of all 121 million workers. The average from this sample is then used as an estimate of the average income for the entire population.

A Statistic Describes a sample and serves as an estimate of the corresponding population parameter.

Example 1.4. The average income of those several thousand workers computed by the Department of Labor is a statistic.

A Variable Is the characteristic of the population that is being examined in the statistical study.

Example 1.5. In a study concerning the income of wage earners in the US, the variable is Income.

Example 1.6. If the statistical advisor for the mayor of San Francisco is interested in the distance commuters must drive each morning, the variable is Miles driven.

A variable can be:

1. A quantitative variable – if the observations can be expressed numerically. For Example, the incomes of all the wage earners is an example of a quantitative population.

2. A qualitative variable is measured nonnumerically. For Example, the marital status of credit applicants, the sex of students, hair color, the race etc.

3. A continuous variable is one that can take on any value within a given range.

4. A discrete variable is restricted to certain values, usually whole numbers. They are often the result of enumeration or counting. The number of students in the class or the number of cars sold by General Motors are the Examples.

1.3.1 Absolute and Relative Statistical Values

Statistics in its resume is based on numerical data. First of all, the results of statistical observation are registered in forms of original Absolute values.

Absolute statistical values are quantitative indexes, which characterize measurement of public activities in particular time and place conditions. Absolute statistical values do not show the structure of public activity under consideration, its progress in time, and do not give a full idea of it.

In statistics all Absolute statistical values Are

1. Denominate numbers (represent measures of factors).

2. Measured in concrete units.

3. Can be positive and negative (income, lost, decrease, etc.).

Measures of factors can be

1. Natural units (lengths, volume, etc.)

– simple (meters, liters, tons, etc.);

– complex – a combination of different units (kilometer per hour, kilowatt per hour, etc.).

2. Pricing units (currency of a country).

3. Labor units (work content of particular operation, etc.).

Absolute statistical values Can be divided on groups:

1. Individual (characterize the factor size of a particular unit).

2. Resultant (summary).

3. Instant values (a real level of an phenomenon on a certain moment or a date, i. e. floating assets, population size, etc.).

4. Interval values (result over a period of time, i. e. population increase over a period of time, quantum of output over a month or a year, etc.).

Relative value in statistics is a deviation part of two values. The Main rule for calculation Of relative values: numerator is a characteristic under the study. It is called Current (reporting) magnitude. The magnitude under the comparison called the Base of comparison or a Base.

The Comparison result of two values of the same name can be expressed as:

1. Coefficient (a quantity of times a current magnitude “less” or “more” of the comparison base).

2. Percent (if a base is 100%).

3. Per thousand (the base is 1,000 units).

4. Per ten thousands (the base is 10,000 units).

Per one hundred thousand (the base is 100,000 units).

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