# Statistical Data Types

Yao Yao on January 8, 2016

Today I feel it necessary to master some stats terms for better discussions of machine learning problems.

However, the concepts are not that unified nor intuitive. Here I’d rather list some examples to illustrate.

The following note is summarized from

There are two types of data:

• Qualitative (定性的)
• Data is qualitative when it is observed and placed into categories, such as gender (male, female), health (healthy, sick), opinion (agree, neutral, disagree).
• 但是 categorical variables 一般等同于 nominal variable.
• Quantitative (定量的)
• Data is quantitative when it is measured with a ruler, jug, weighing scales, stop-watch, thermometer and so on.
• Quantitative data are data about numeric variables.

Divided further:

• Qualitative (categorized)
• Ordinal
• Nominal / Categorical
• Quantitative (measured / numeric)
• Ratio
• Interval

## 1. Nominal / Categorical

nominal: [ˈnɒmɪnl], of name

• (of a role or status) existing in name only.
• (of a price or amount of money) very small; far below the real value or cost.

• Gender := male / female …
• Animal := pig / sheep / horse …

## 2. Ordinal

E.g.

• Is your general health := poor / reasonable / good / excellent
• Is your annual salary := low / average / high

• 政治上是不平等的，可以看到明显的差距；
• 有差距似乎意味着可以做减法，但是这里做减法是没有意义的。E.g. you tell me how much is high - low?

## 3. Interval

E.g.

• (discrete) hours := 1am / 2am / … / 12pm / 1pm / 2pm …
• (continuous) Celsius (or Fahrenheit) temperature := 10°C / 20°C / 30°C …

• years in calendar := 1900 A.D. / 2000 A.D. …
• years elapsed := 1 / 2 / 3 …

• 2000 A.D. 比 1000 A.D. 晚 1000 年
• 2000 A.D. 并不表示 1000 A.D. 的两倍

• 2 years 比 1 year 要长 1 year
• 2 years 的时间的确是 1 year 的两倍

## 4. Ratio

• 既可以做减法
• 也可以做除法

E.g.

• Kalvin temperature := 10K / 20K / 30K …
• Weight := 1 lb / 2 lb …
• Height := 1 inch / 2 inches …