1
Key Terms and Concepts in Statistics
1. Random Variable
o An attribute or characteristic of interest on which data is collected and
analysed.
2. Data
o Actual values (numbers) or outcomes recorded on a random variable.
o Data are unprocessed, raw facts and are meaningless without analysis.
3. Information
o The results obtained from processing data, which give it meaning.
4. Sample
o A subset or fraction of a population selected for analysis or to conduct a
survey.
o Researchers use samples instead of the full population to:
1. Save on costs.
2. Address time constraints.
3. Overcome practical challenges in studying the entire population.
5. Sampling Unit
o The object being measured, counted, or observed with respect to the
random variable.
o Example: s include a consumer, employee, household, company, or
product.
6. Population
o The entire set of possible data values for the random variable under
study.
7. Population Parameter
o A measure describing a characteristic of the population, such as a
population average or proportion.
o It uses all population data values to compute its value.
8. Sample Statistic
o A measure describing a characteristic of a sample, such as a sample
average or proportion.
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Table 1.2. below shows some of the statistics and parameter symbols that will be used
in this subject.
Data Types
1. Random Variable
o Can be qualitative (categorical) or quantitative (numeric).
2. Qualitative Random Variables
o Generate categorical (non-numeric) data.
o Data represented by categories (labels, not numbers).
o Example: s:
▪ Gender of a consumer (male or female).
▪ Employee’s highest qualification (matric, diploma, degree).
3. Quantitative Random Variables
o Generate numeric data.
o Real numbers that can be manipulated using arithmetic operations
(addition, subtraction, multiplication, division).
o Example: s:
▪ Age of an employee (e.g., 46 years, 28 years, 32 years).
▪ Machine downtime (e.g., 8 min, 32.4 min, 12.9 min).
▪ Price of a product in different stores (e.g., R6.75, R7.45, R7.20).
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4. Numeric Data Classification:
o Discrete Data: Whole numbers (integers).
▪ Example: s:
▪ Number of students in a class (e.g., 24, 37, 41).
▪ Number of cars sold by a dealer in a month (e.g., 14, 27,
21).
o Continuous Data: Can take any value within a range.
▪ Example: s:
▪ Assembly time for a part (e.g., 28.4 minutes within a range
of 27–31 minutes).
▪ Mass of hand luggage (e.g., 2.4 kg between 0.5 kg and 10
kg).
Data Measurement Scales
1. Nominal Data
o Categorical data with no order or ranking.
o Categories are of equal importance and can only be counted.
o Example: s:
▪ Gender (1 = male, 2 = female).
▪ City of residence (1 = PTA, 2 = DBN, 3 = CT, 4 = BFN).
2. Ordinal Data
o Categorical data with a clear order or ranking between categories.
o Differences between categories are not equal, but order matters.
o Example: s:
▪ Clothing sizes (1 = small, 2 = medium, 3 = large, 4 = X-large).
▪ Product usage level (1 = light, 2 = moderate, 3 = heavy
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3. Interval Data
o Numeric data where both order and distance between values matter, but
there is no true zero.
o Typically generated from rating scales (e.g., surveys).
o Example: s:
▪ Temperature scales (e.g., 20°C, 25°C, 30°C).
▪ Likert scale ratings (e.g., 1 = strongly disagree, 5 = strongly
agree).
4. Ratio Data
o Numeric data with all the properties of numbers: order, distance, and an
absolute zero.
o Ratios between numbers are meaningful, and all arithmetic operations
can be performed.
o Example: s:
▪ Employee ages (years).
▪ Customer income (R).
▪ Distance travelled (km).
▪ Product mass (g).
Data Measurement Scales
1. Ratio Data
o Has all the properties of numbers: order, measurable difference, and a
true zero starting point.
o Ratios between values can be computed and have meaningful
interpretations.
▪ Example: s:
▪ 5 is half of 10.
▪ 36 is twice as much as 18.
o Strongest data for statistical analysis, as it allows the extraction of the
most statistical information compared to other data types.
Key Terms and Concepts in Statistics
1. Random Variable
o An attribute or characteristic of interest on which data is collected and
analysed.
2. Data
o Actual values (numbers) or outcomes recorded on a random variable.
o Data are unprocessed, raw facts and are meaningless without analysis.
3. Information
o The results obtained from processing data, which give it meaning.
4. Sample
o A subset or fraction of a population selected for analysis or to conduct a
survey.
o Researchers use samples instead of the full population to:
1. Save on costs.
2. Address time constraints.
3. Overcome practical challenges in studying the entire population.
5. Sampling Unit
o The object being measured, counted, or observed with respect to the
random variable.
o Example: s include a consumer, employee, household, company, or
product.
6. Population
o The entire set of possible data values for the random variable under
study.
7. Population Parameter
o A measure describing a characteristic of the population, such as a
population average or proportion.
o It uses all population data values to compute its value.
8. Sample Statistic
o A measure describing a characteristic of a sample, such as a sample
average or proportion.
, 2
Table 1.2. below shows some of the statistics and parameter symbols that will be used
in this subject.
Data Types
1. Random Variable
o Can be qualitative (categorical) or quantitative (numeric).
2. Qualitative Random Variables
o Generate categorical (non-numeric) data.
o Data represented by categories (labels, not numbers).
o Example: s:
▪ Gender of a consumer (male or female).
▪ Employee’s highest qualification (matric, diploma, degree).
3. Quantitative Random Variables
o Generate numeric data.
o Real numbers that can be manipulated using arithmetic operations
(addition, subtraction, multiplication, division).
o Example: s:
▪ Age of an employee (e.g., 46 years, 28 years, 32 years).
▪ Machine downtime (e.g., 8 min, 32.4 min, 12.9 min).
▪ Price of a product in different stores (e.g., R6.75, R7.45, R7.20).
, 3
4. Numeric Data Classification:
o Discrete Data: Whole numbers (integers).
▪ Example: s:
▪ Number of students in a class (e.g., 24, 37, 41).
▪ Number of cars sold by a dealer in a month (e.g., 14, 27,
21).
o Continuous Data: Can take any value within a range.
▪ Example: s:
▪ Assembly time for a part (e.g., 28.4 minutes within a range
of 27–31 minutes).
▪ Mass of hand luggage (e.g., 2.4 kg between 0.5 kg and 10
kg).
Data Measurement Scales
1. Nominal Data
o Categorical data with no order or ranking.
o Categories are of equal importance and can only be counted.
o Example: s:
▪ Gender (1 = male, 2 = female).
▪ City of residence (1 = PTA, 2 = DBN, 3 = CT, 4 = BFN).
2. Ordinal Data
o Categorical data with a clear order or ranking between categories.
o Differences between categories are not equal, but order matters.
o Example: s:
▪ Clothing sizes (1 = small, 2 = medium, 3 = large, 4 = X-large).
▪ Product usage level (1 = light, 2 = moderate, 3 = heavy
, 4
3. Interval Data
o Numeric data where both order and distance between values matter, but
there is no true zero.
o Typically generated from rating scales (e.g., surveys).
o Example: s:
▪ Temperature scales (e.g., 20°C, 25°C, 30°C).
▪ Likert scale ratings (e.g., 1 = strongly disagree, 5 = strongly
agree).
4. Ratio Data
o Numeric data with all the properties of numbers: order, distance, and an
absolute zero.
o Ratios between numbers are meaningful, and all arithmetic operations
can be performed.
o Example: s:
▪ Employee ages (years).
▪ Customer income (R).
▪ Distance travelled (km).
▪ Product mass (g).
Data Measurement Scales
1. Ratio Data
o Has all the properties of numbers: order, measurable difference, and a
true zero starting point.
o Ratios between values can be computed and have meaningful
interpretations.
▪ Example: s:
▪ 5 is half of 10.
▪ 36 is twice as much as 18.
o Strongest data for statistical analysis, as it allows the extraction of the
most statistical information compared to other data types.
