Statistics Lecture

September 21, 2011

Variables and Data

•A variable is a characteristic of a population that changes or

varies over time; its something that can be measured over time

oEx. How household income changes in a region or country

over time

oTwo key categories: quantitative and qualitative

•Quantitative variables: can be discrete [1,2,3,4,5, etc] or

continuous [1.7, 2.76, 4.45, etc] in continuous data, the

decimals matter

•Qualitative data don’t have numbers; ex. Male or female, plant

species, etc.

•Data: results from measuring variables [use data as the plural]

oMultivariate, bivariate and univariate

Scales of Measurement

•A scale defines the amount of information a variable contains

and what statistical techniques can be used

•Four scales: nominal [lowest amount of information], ordinal,

interval and ratio [highest amount of information]

oNominal: lowest scale and no numerical value attached to

it [no weighting]. Classifies observations into mutually

exclusive [an element can only go into one box or another;

only one category] and collectively exhaustive groups. A

nominal variable is simply the name or category of the

variable [ex. Its either male or female]

oOrdinal: allows data to be ordered and ranked. Ex. People

living in large towns, medium towns or small towns and

could then group them by the top 12 cities for example.

oInterval: unit distance separating numbers is important. Ex.

Temperature [F or C] or taxable income [$] In this case,

negative numbers can mean something

oRatio: ratios of distance on a number scale. Most important

way of describing it is the presence of an absolute zero;

you can’t have less than zero on a ratio but zero is

possible. Ex. Temperature [Kelvin], income from all sources

[$], population of a city. In practice, we consider

interval/ratio scales together

Describing Data

## Document Summary

Variables and data: a variable is a characteristic of a population that changes or varies over time; its something that can be measured over time, ex. Male or female, plant species, etc: data: results from measuring variables [use data as the plural, multivariate, bivariate and univariate. Classifies observations into mutually exclusive [an element can only go into one box or another; only one category] and collectively exhaustive groups. A nominal variable is simply the name or category of the variable [ex. Its either male or female: ordinal: allows data to be ordered and ranked. People living in large towns, medium towns or small towns and could then group them by the top 12 cities for example: interval: unit distance separating numbers is important. Temperature [f or c] or taxable income [$] in this case, negative numbers can mean something: ratio: ratios of distance on a number scale.