Qualitative vs. Quantitative - Algebra-1

1. Fundamental Concepts

Qualitative Data: Data used to describe the nature, characteristics, or categories of things. It cannot be measured by numerical values, mainly focuses on "what it is", and emphasizes distinguishing the attributes of things.
Quantitative Data: Data presented in numerical form, which can be measured and counted. It mainly focuses on "how much" and can be used for mathematical operations and statistical analysis.

Characteristics of Qualitative Data:
- Non-numerical, usually presented as words, symbols, or categories.
- Used to distinguish different attributes or characteristics, such as color, gender, occupation, etc.
- Cannot directly perform mathematical operations such as addition, subtraction, multiplication, and division. When analyzing, methods such as classification and counting are often used.
Characteristics of Quantitative Data:
- Numerical, with clear quantitative meaning.
- Can be obtained through measurement or counting, such as height, weight, age, score, etc.
- Can perform various mathematical operations and statistical processing, such as calculating average, variance, etc.
Relationship Between the Two: Qualitative data and quantitative data are two basic classifications of data. In actual statistical analysis, they may be used in combination to comprehensively describe the research object.

1:
- Qualitative: Students' gender (male, female), types of fruits (apple, banana, orange).
- Quantitative: The age of students in a class (12 years old, 13 years old, 14 years old), the weight of a bag of apples (500g, 600g, 700g).
2:
- Qualitative: Employees' job satisfaction levels (very satisfied, satisfied, average, dissatisfied, very dissatisfied), types of books (novel, popular science, history).
- Quantitative: Monthly salaries of employees in a company (3,000 yuan, 4,500 yuan, 6,000 yuan), annual rainfall in a certain area (800mm, 900mm, 1000mm).
3:
- Qualitative: Keywords of consumers' evaluations of a new product (easy to use, beautiful appearance, low cost performance, complicated operation), types of people's values in different cultural backgrounds (collectivism, individualism, etc.).
- Quantitative: Daily closing prices of a stock within a year (100 yuan, 105 yuan, 98 yuan, etc.), various sports indicators of an athlete in multiple competitions (running speed, high jump height, long jump distance, etc.).

Distinguishing Between Qualitative and Quantitative Data:
- First, judge whether the data is in numerical form. If yes, it may be quantitative data; if it is in non-numerical form such as words or categories, it may be qualitative data.
- Further verification: Quantitative data can be used for mathematical operations (such as calculating the average), while qualitative data cannot.
Selection of Application Scenarios:
- When the research purpose is to describe the attributes, characteristics of things or conduct classification, qualitative data is adopted.
- When the research purpose is to measure quantities, compare sizes, or conduct quantitative analysis, quantitative data is adopted.
Analysis Methods:
- Qualitative Data: Methods such as classification and summarization, frequency statistics, and making pie charts or bar charts can be used for analysis to show the distribution of different categories.
- Quantitative Data: Statistical quantities such as average, median, variance, and standard deviation can be calculated, and histograms, line charts, etc. can be drawn for analysis to reveal the central tendency, dispersion degree, and change rules of the data.