Type of Variable & ratio

Types of variables

All data generated by measurement, surveys, research, etc. can be variables and also use the term feature in machine learning. An event contains multiple variable values and is called an instance. The following table contains three variables: name, age, gender, height, and three events: instances. A typical form of data, each variable consists of a column and an instance of a row, which is called a dataset.

name	age	sex	height
A	10	male	153
B	15	female	161
C	21	male	181

In constructing a dataset, the number of questions equals the number of variables, and the number of respondents affects the number of observations. However, the number of respondents does not affect the number of variables.
As shown in Table 1.1, all variables are separated by categorical variables and quantitative variables, and variables are separated by nominal, ordinal, discrete, and continuous, depending on the measurement level.

Types of variables

Variable	Contents	Level
Categorical variables	Group(Class)	Nominal
	Ordinal
Quantitative variables	Quantity(Size)	Discrete
Continuous

Nominal variables are variables that can only be qualitative classified without logical order. For example, for a dataset of fruits, 1=apples, 2=folds, and 3=watermelons, each fruit is numbered 1, 2 and 3, but the fruit is logically irrelevant between rank and other values. You can only give a name.

Movies can be ranked using rating data that is given within a certain range. However, ratings are subjective evaluations and the intervals between each rating are not constant either. These variables are called ordinal variables.

For quantitative variables, measurement levels have their own ranks, and differences between them are measurable and interrelated. Also, the figure itself is meaningful. Therefore, for the same level, it has the same meaning. For these measurement levels, they are divided into countable variables and uncountable parts, respectively, called discrete and continuous. Discrete refers to a form that can be represented as an integer, such as a population belonging to a certain group, and continuous refers to a form of proportion to absolute criteria such as temperature, height, weight, etc.

Example 1)
  Determine the measurement level of the following variables:

• Age: discrete, there is a clear measure of measurement, and the difference between ages is meaningful.
• Party Name: Nominal, this variable can only classify names.
• Weight: Continuous, absolute reference value 0 exists. You can generate figures proportionally based on zero, but you cannot represent them in clear numbers, such as natural numbers or integers.
• If students are grouped into three groups A, B, and C, the variable 'group': nominal
• If players A, B, and C are participating in steps 5, 2 and 3 respectively, then the variable "Step": ordinal. For this variable, the differences within or between steps are not necessarily equal.
• The movie was evaluated on a 5-point scale such as very good, good,... The level of the variable in this outcome: ordinal, in this survey, ordinal number are important. However, the difference between those intervals is not equal.
• City Name: Nominal. You can just give it a name, but you can't rank it.
• People's bank balances: continuous. The difference between each value is the same, and the value itself has meaning.

ratio

Distinguish between absolute and relative proportions.

• absolute proportion: part of a whole
• Relative Ratio: Increase or decrease relative to another ratio

The reason for the news that a city is not safe with the increase in crime cases is probably the rate of increase. If this news is added with information about a 50% increase in the homicide rate, it gives the basis for the news that it will get worse, but it's still incomplete. Its incompleteness is due to the lack of information about the number of events being compared, such as an increase from 2 to 3 or an increase from 10 to 4. That is, an increase of 50% is for an increase over the number of past events. Previous figures are needed for complete information. In this case, 50% is a relative ratio, and information about the absolute ratio is needed to fully understand this news. For example, in a city with a population of 100,000 people, if 3 cases occurred compared to 2 cases in the previous year, the increase would be 50%, but an absolute increase of 0.2% to 0.3% would significantly weaken the basis of the negative news. As such, the meaning of relative and absolute ratios is very important, and reporting only relative ratios should be avoided.

The following shows the change in population density in Seoul and the neighboring metropolitan area, and unlike the above case, a clear trend is shown by the relative ratio.

	Seoul	neighboring
Year	Density	Relative ratio(%)	Density	Relative ratio(%)
2106	16263	-	25350	-
2017	16136	-0.78	25476	0.50
2018	16034	-0.63	25675	0.78
2019	15964	-0.44	25844	0.66