Question 1 — Data Definition
Data can be defined as:
A. A form of information representation
B. A subjective opinion
C. The research result
D. A research method
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A. A form of information representation 数据是信息的表现形式📝 点击查看解析
English: Data are objective records of phenomena, serving as a representation of information, not subjective opinions or research methods. 中文：数据是对现象的客观记录，是信息的表现形式，而不是主观意见或研究方法。Question 2 — What is Not Data
Which of the following is NOT data?
A. Student grades
B. Temperature changes
C. Population size
D. Teaching methods of teachers
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D. Teaching methods of teachers 教师的教学方法📝 点击查看解析
English: Grades, temperatures, and population sizes can be measured and recorded as data, while “teaching methods” are approaches, not data itself. 中文：成绩、气温、人口数可以被记录为数据，而“教学方法”是一种方式，不是数据本身。Question 3 — Elements in a Survey
In a survey of college students’ spending, each student surveyed is considered a(n):
A. Data
B. Element
C. Variable
D. Observation
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B. Element 要素📝 点击查看解析
English: Each student is the object being studied (an element), while their spending amount is a variable. 中文：每个学生是研究对象，称为要素；他们的消费金额才是变量。Question 4 — Elements in a Company Survey
In a company survey on job satisfaction, each employee is a(n): ______.
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Element 要素📝 点击查看解析
English: In the survey, the unit being studied (employee) is the element. 中文：在调查中，研究的对象（员工）就是要素。Question 5 — Quantitative Variable
Which of the following is a quantitative variable?
A. Gender
B. Age
C. Occupation
D. Blood type
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B. Age 年龄📝 点击查看解析
English: Age is measurable and numerical, hence quantitative. Gender, occupation, and blood type are qualitative. 中文：年龄是可度量的数值型变量，因此是定量变量；性别、职业和血型是定性变量。Question 6 — Qualitative vs Quantitative
Identify the qualitative and quantitative variables in the set: {Grade level, Major, Exam score}.
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Qualitative: Grade level, Major Quantitative: Exam score 定性变量：年级、专业；定量变量：成绩📝 点击查看解析
English: Grade level and major are qualitative (categorical). Exam score is numerical, hence quantitative. 中文：年级和专业是定性（分类），成绩是数值型，因此是定量变量。Question 7 — Observations
A questionnaire records: “Zhang San, Male, 22, Marketing major, Junior year.” This whole record is a(n):
A. Element
B. Observation
C. Data
D. Variable
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B. Observation 观测值📝 点击查看解析
English: The complete record of an element is called an observation. 中文：对一个要素的完整记录称为观测值。Question 8 — Dataset Rows
In a dataset table, each row usually represents a(n):
A. Element
B. Variable
C. Observation
D. Scale
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C. Observation 观测值📝 点击查看解析
English: Each row contains all measurements for one element, hence it is an observation. 中文：表格中的每一行包含一个研究对象的全部信息，因此是一条观测值。Question 9 — Nominal Scale
Which of the following is nominal data?
A. Blood type (A, B, AB, O)
B. Grade level (Excellent, Good, Pass, Fail)
C. Celsius temperature
D. Income
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A. Blood type 血型📝 点击查看解析
English: Blood type is a categorical label without order, making it nominal. 中文：血型只是分类，没有顺序关系，因此属于名义尺度。Question 10 — Phone Number Scale
Why is a phone number nominal scale data?
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Because it is only an identifier, not a measure of quantity or order. 因为它只是一个识别符，而不是数量或顺序的度量。📝 点击查看解析
English: Phone numbers are used to identify subscribers. They cannot express magnitude, difference, or ratio. 中文：电话号码用于识别用户，不能表示大小、差异或比例关系。Question 11 — Ordinal Scale
Which is ordinal scale data?
A. Student ID
B. Competition ranks (1st, 2nd, 3rd)
C. Height
D. Weight
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B. Competition ranks (1st, 2nd, 3rd) 比赛名次（第一名、第二名、第三名）📝 点击查看解析
English: Competition ranks indicate order but not equal intervals, so they are ordinal data. 中文：比赛名次有顺序，但名次之间的间距不一定相等，因此属于顺序尺度。Question 12 — Customer Satisfaction Scale
Customer satisfaction levels (Very dissatisfied → Very satisfied) belong to which scale? Why?
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Ordinal scale, because it indicates order but not equal differences. 顺序尺度，因为它表示顺序，但不同等级间差距不一定相等。📝 点击查看解析
English: Satisfaction levels show order (from low to high), but the distance between “satisfied” and “very satisfied” is not necessarily the same as between “neutral” and “satisfied.” 中文：满意度水平有从低到高的顺序，但“满意”到“非常满意”的差距不一定等于“一般”到“满意”的差距。Question 13 — Interval Scale
Celsius temperature belongs to:
A. Nominal
B. Ordinal
C. Interval
D. Ratio
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C. Interval 区间尺度📝 点击查看解析
English: Celsius has equal intervals but its zero is arbitrary, not a true zero. 中文：摄氏温度有相等的间距，但零点是人为规定的，不是真正的零点。Question 14 — Calendar Years
Why are calendar years (e.g., 2000, 2020) interval scale, not ratio scale?
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Because the difference between years is meaningful, but year “0” is not a true zero. 因为年份之间的差异有意义，但“公元0年”不是真正的零点。📝 点击查看解析
English: We can say 2020 is 20 years after 2000, but we cannot say 2000 is “twice” 1000. 中文：我们可以说2020比2000晚20年，但不能说2000是1000的“两倍”。Question 15 — Ratio Scale
Which of the following is NOT ratio data?
A. Income
B. Age
C. Celsius temperature
D. Height
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C. Celsius temperature 摄氏温度📝 点击查看解析
English: Income, age, and height have a true zero and allow ratio comparisons. Celsius zero is arbitrary. 中文：收入、年龄和身高都有真实的零点，可以进行比例比较；摄氏温度的零点是人为规定的。Question 16 — Salary as Ratio Scale
Why is salary considered ratio scale data?
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Because it has a true zero (zero income) and ratios like “twice as much” are meaningful. 因为薪资有真实零点（零收入），并且可以说一个人收入是另一个人的两倍。📝 点击查看解析
English: Salary is continuous, measurable, and starts at zero, making ratios valid. 中文：薪资是连续可度量的，从零开始，因此比例比较有效。Question 17 — Student Record Analysis
A student record includes:
- ID: 202501
- Name: Li Hua
- Gender: Male
- Age: 21
- Major: Accounting
- Grade: 88
Answer:
- What is the element?
- What are the variables?
- Which scale does each variable belong to?
- What is the observation?
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1. Element: Li Hua (student) / 李华（学生） 2. Variables: ID, Name, Gender, Age, Major, Grade 3. Scales: - ID (Nominal) - Name (Nominal) - Gender (Nominal) - Age (Ratio) - Major (Nominal) - Grade (Ratio/Interval depending on definition) 4. Observation: The full record above 观测值：这条完整记录📝 点击查看解析
English: The element is the student (Li Hua). Variables include ID, name, gender, age, major, and grade. Each variable belongs to a scale. The complete record is the observation. 中文：要素是学生李华；变量包括学号、姓名、性别、年龄、专业和成绩；每个变量对应一种尺度。这条完整的记录就是一个观测值。Question 18 — City Survey
A survey records data from 10 cities:
- Population
- City name
- City size (large, medium, small)
- Average annual temperature
Classify the variable types and scales.
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- Population: Quantitative, Ratio - City name: Qualitative, Nominal - City size: Qualitative, Ordinal - Temperature: Quantitative, Interval📝 点击查看解析
English: Population has a true zero, so ratio; city name is just a label, nominal; city size has order, ordinal; temperature has equal intervals but arbitrary zero, interval. 中文：人口有真实零点，属于比率尺度；城市名称是标签，属于名义尺度；城市规模有顺序，属于顺序尺度；气温有相等间距但零点任意，属于区间尺度。Question 19 — Variable Classification
Classify the following variables: Blood type, Height, Exam score, Customer ranking.
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- Blood type: Nominal - Height: Ratio - Exam score: Interval/Ratio - Customer ranking: Ordinal📝 点击查看解析
English: Blood type is categorical without order (nominal). Height has a true zero (ratio). Exam scores can be treated as interval or ratio depending on context. Ranking has order but no equal gaps (ordinal). 中文：血型是没有顺序的分类（名义）；身高有真实零点（比率）；成绩可按区间或比率处理；排名有顺序但间距不等（顺序）。Question 20 — Observations vs Variables
In a dataset of 50 students’ test scores, each student is a(n) ______, and each test score is a(n) ______.
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Each student is an element, and each test score is a variable. 每个学生是要素，每个成绩是变量。📝 点击查看解析
English: The student is the entity being studied (element), while the score is a measurable characteristic (variable). 中文：学生是研究对象（要素），成绩是可度量的特征（变量）。Question 21 — Data Types
Which of the following is quantitative data?
A. Marital status
B. Favorite color
C. Number of siblings
D. Nationality
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C. Number of siblings 兄弟姐妹数量📝 点击查看解析
English: Number of siblings can be measured numerically, so it is quantitative. The others are categorical (qualitative). 中文：兄弟姐妹的数量可以用数值衡量，因此是定量数据；其他都是分类变量（定性）。Question 22 — Elements in Research
In a medical study testing the effect of a new drug, each patient is a(n):
A. Variable
B. Observation
C. Element
D. Dataset
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C. Element 要素📝 点击查看解析
English: Each patient is the entity being studied, so they are elements. Their blood pressure, weight, etc., are variables. 中文：每个病人是研究的对象，因此是要素；他们的血压、体重等是变量。Question 23 — Variables in a Company
A company collects data on: Employee ID, Department, Monthly Salary, Years of Service.
Classify each variable’s scale.
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- Employee ID: Nominal - Department: Nominal - Monthly Salary: Ratio - Years of Service: Ratio📝 点击查看解析
English: ID and department are labels (nominal). Salary and years of service both have true zero points, so ratio. 中文：工号和部门是标签（名义尺度）；薪水和工龄有真实零点，因此是比率尺度。Question 24 — Observations in a Dataset
A dataset contains survey results from 500 customers. Each row in the dataset represents a(n):
A. Variable
B. Element
C. Observation
D. Scale
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C. Observation 观测值📝 点击查看解析
English: Each row corresponds to one customer’s full data record, so it is an observation. 中文：每一行记录了一个顾客的完整信息，因此是一条观测值。Question 25 — Nominal vs Ordinal
Which of the following is ordinal data rather than nominal?
A. Student major (Accounting, Marketing, Finance)
B. Education level (High school, Bachelor, Master, PhD)
C. Country of origin
D. Employee ID
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B. Education level (High school, Bachelor, Master, PhD) 教育水平（高中、本科、硕士、博士）📝 点击查看解析
English: Education level has a natural order (higher education means higher level). The others are categories without order. 中文：教育水平有自然顺序（学历越高级别越高）；其他变量只是分类，没有顺序。Question 26 — Interval Scale Case
Which of the following is measured on an interval scale?
A. Annual income
B. Kelvin temperature
C. IQ scores
D. Number of products sold
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C. IQ scores 智商分数📝 点击查看解析
English: IQ scores have equal intervals but no true zero, so interval. Income, products sold are ratio; Kelvin has a true zero, so ratio. 中文：智商分数有相等的间距但没有真实零点，因此是区间尺度；收入和销量是比率尺度；开尔文温度有真实零点，也是比率尺度。Question 27 — Ratio Scale Example
Which situation best illustrates ratio scale measurement?
A. Ranking top 5 restaurants
B. Recording the year of graduation
C. Measuring students’ height in centimeters
D. Rating a movie from 1 to 5 stars
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C. Measuring students’ height in centimeters 学生身高（厘米）📝 点击查看解析
English: Height has a true zero and ratios (e.g., one student is twice as tall) are meaningful, so ratio scale. 中文：身高有真实零点，比例比较有意义（一个学生可能是另一个的两倍高），因此是比率尺度。Question 28 — Identify Scales
Identify the scale of measurement:
- Political party affiliation
- Exam percentage score
- Customer satisfaction ranking
- Daily sales revenue
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- Political party: Nominal - Exam percentage: Ratio/Interval (depends on grading system) - Satisfaction ranking: Ordinal - Sales revenue: Ratio📝 点击查看解析
English: Party affiliation is just a label (nominal). Exam percentage may be treated as interval or ratio. Ranking shows order (ordinal). Sales revenue has a true zero (ratio). 中文：政党归属只是标签（名义）；考试分数通常按区间处理，有时也可比率；满意度排名体现顺序（顺序）；销售收入有真实零点（比率）。Question 29 — Observation vs Variable
True or False: In a dataset, each column usually represents an observation, while each row represents a variable.
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False 错误📝 点击查看解析
English: In a dataset, each column represents a variable, and each row represents an observation. 中文：在数据集中，每一列是一个变量，每一行是一条观测值。Question 30 — Mixed Example
A marketing survey collects: Customer name, Gender, Age, Favorite brand, Monthly spending.
Classify each variable.
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- Customer name: Nominal - Gender: Nominal - Age: Ratio - Favorite brand: Nominal - Monthly spending: Ratio📝 点击查看解析
English: Name, gender, brand are identifiers (nominal). Age and spending have true zeros, so ratio. 中文：姓名、性别、品牌只是标签（名义）；年龄和消费有真实零点，因此是比率尺度。Question 33 — Market Research Case
A marketing survey collects data:
| Customer | Age | Favorite Brand | Satisfaction (1–5) | Monthly Spending ($) |
|---|---|---|---|---|
| C01 | 25 | Nike | 4 | 200 |
| C02 | 32 | Adidas | 5 | 350 |
| C03 | 28 | Puma | 3 | 150 |
Answer:
- What are the observations?
- Which variables are qualitative and which are quantitative?
- Classify the measurement scale of Satisfaction.
📖 点击查看答案
1. Observations: Each customer’s row of data (3 in total) 2. Qualitative: Customer, Favorite Brand Quantitative: Age, Satisfaction, Monthly Spending 3. Satisfaction is Ordinal (1–5 ratings with order but not equal intervals)📝 点击查看解析
English: Each row = observation. Brand is qualitative, age/spending are ratio. Satisfaction is ordinal since it ranks satisfaction levels but the difference between 3 and 4 may not equal 4 and 5. 中文：每一行是观测值；品牌是定性变量，年龄和消费是比率尺度；满意度是顺序尺度，因为分数有顺序但间隔不一定相等。Question 34 — Temperature and Geography
A dataset includes:
| City | Average Temperature (°C) | Elevation (m) | Region |
|---|---|---|---|
| A | 18 | 300 | East |
| B | 25 | 50 | South |
| C | 10 | 1200 | West |
Answer:
- Identify the element.
- Determine the variables.
- Assign the correct scale for Temperature and Elevation.
📖 点击查看答案
1. Elements: Cities (A, B, C) 2. Variables: City, Temperature, Elevation, Region 3. Temperature: Interval (arbitrary zero) Elevation: Ratio (true zero at sea level)📝 点击查看解析
English: The city is the element. Variables include name, temperature, elevation, and region. Temperature is interval, elevation is ratio. 中文：城市是要素；变量包括城市名、温度、海拔和地区。温度是区间尺度，海拔是比率尺度。Question 35 — Sports Ranking Case
A sports dataset shows:
| Athlete | Sport | Country | Rank | Score |
|---|---|---|---|---|
| P1 | Tennis | USA | 1 | 95 |
| P2 | Football | Brazil | 2 | 89 |
| P3 | Basketball | Spain | 3 | 85 |
Answer:
- Which variable is ordinal?
- Which variable is ratio?
- How many observations are there?