## Lesson 5: Statistic Variables (I).

January 17, 2012I Have to Know by the End of this Lesson

**1. Introduction**

The word ‘Statistics’ is derived from the Latin word ‘Statis’ which means a **“political state.”** Clearly, statistics is closely linked with the administrative affairs of a state such as facts and figures regarding defence force, population, housing, food, financial resources etc. What is true about a government is also true about industrial administration units, and even one’s personal life.

The word statistics has several meanings. In the first place, it is a **plural noun** which describes a collection of numerical data such as employment statistics, accident statistics, population statistics, birth and death, income and expenditure, of exports and imports etc. It is in this sense that the word ‘statistics’ is used by a layman or a newspaper.

Secondly the word statistics as a **singular noun** is used to describe a branch of applied mathematics, whose purpose is to provide methods of dealing with a collection of data and extracting information from them in compact form by tabulating, summarizing and analyzing the numerical data or a set of observations. In this case it is written “Statistics” with capital letter.

The word **‘Statistics’** in the second sense is defined as follows:-

“The collection, presentation, analysis and interpretation of numerical data.”

**1.1. Statistical terms**

**Statistics/** **Estadísticas. **Statistics is the use of data to help the decision maker to reach better decisions.

**Data/ Datos. **It is any group of measurements that interests us. These measurements provide information for the decision maker. The data that reflects non-numerical features or qualities of the experimental units, is known as qualitative data. The data that possesses numerical properties is known as quantitative data.

**Population/Población. **Any well defined set of objects about which a statistical enquiry is being made is called a population or universe.The total number of objects (individuals) in a population is known as the size of the population. This may be finite or infinite.

**Individual/Individuo .**Each object belonging to a population is called as an individual of the population.

**Sample/Muestra .**A finite set of objects drawn from the population with a particular aim, is called a sample.The total number of individuals in a sample is called the **sample size**.

**Statistical variable/Variable estadística. **The information required from an individual, from a population or from a sample, during the statistical enquiry (survey) is known as the statistical variable. It is either numerical or non-numerical. For e.g. the size of shoes is a numerical variable which refers to a quantity, whereas the mother tongue of a person is a non-numerical variable which refers to a quality. Thus we have quantitative and qualitative types of variables.

**1.2. Types of statistical variables**

Statistical variables may be classified as **either quantitative or qualitative**:

Type | Definition | Example |

Qualitative |
A variable that is expressed in categories rather than numbers. It has no natural sense of ordering. | The mother tongue of a person, the colour of the eyes or the hair colour of a person |

Quantitative |
A variable of an individual which can be expressed numerically. It may take different values at different times, places, or situations. Data measures either how much or how many of something |
The height of a person, the number of members of a family |

**Quantitative data** **or quantitative variables** can be divided into:

Type | Definition | Example |

Discrete variables |
The set of all possible values which consists only of isolated points, e.g. counting variables (1, 2, 3 …). | The number of children in a class |

Continuous variables |
The set of all values which consists of intervals, e.g. 0-9, 10-19, 20-29… etc. | The weight of a person |

**Qualitative data or qualitative variables** can be divided into:

Type | Definition | Example |

Nominal variables |
Variables with no inherent order or ranking sequence, e.g. numbers used as names (group 1, group 2…) |
Gender, race |

Ordinal variables |
Variables with an ordered series |
“Greatly dislike, moderately dislike, indifferent, moderately like, greatly like”. Numbers assigned to such variables indicate rank order only – the “distance” between the numbers has no meaning. |

**EXERCISE **

This is a list of statistical variables. Classify them and post your answer.

Individual |
Characteristic we are studying (Variable) |
|||

1. A person |
Waist in cm | ® | ||

Colour of skin | ® | |||

Age | ® | |||

Weight in lbs | ® | |||

Sex | ® | |||

Mother tongue | ® | |||

Marks in statistics | ® | |||

2. Mr. Brown’s family |
Number of members | ® | ||

Monthly income in dollars | ® | |||

3. A washer |
Diameter and thickness in cm | ® | ||

Defective or non-defective | ® |

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