LGT5101 Chap.1 Statistical Questions, Data Types and Samples
Statistical Questions, Data Types and Samples
Start with the row
A statistical analysis begins by naming what one row represents and which property is recorded. The experimental unit prevents mixed levels: a row describing a delivery cannot silently be treated as a customer or a depot. Population and sample then fix the scope.
Observations can describe the captured units directly, but extending a result to future or unobserved units requires a sampling argument and stable operating conditions.
Classify by permissible meaning
Variable type controls the honest operations. Nominal labels support counts and category comparisons. Ordinal values preserve order without guaranteeing equal gaps.
Interval values support meaningful differences, while ratio values also have a genuine zero and meaningful ratios. Digits alone do not make a variable quantitative: a depot code remains a label, and a satisfaction score can remain ordinal.
Explain what addition, subtraction or division would mean in context before selecting a summary.
Let the question determine scope
A complete dataset can be a population for one question and a sample for another. Every employee in one branch is the population for a claim about that branch, yet only a sample for a company-wide claim.
Similarly, a variable can be retained quantitatively or grouped into categories when the management question changes. Record that treatment explicitly because grouping loses detail and can alter the visible pattern.
Build an auditable opening
Begin each analysis with five items: experimental unit, target population, observed sample, variables and intended inference.
Then identify primary or secondary data and any filters or missing values. Primary data were collected for the present purpose; secondary data may still be useful, but their definitions and collection process must be checked. This opening is not decorative vocabulary.
It determines whether later frequencies, means and probability models describe the intended decision and whether the final conclusion stays inside the evidence boundary.
What this chapter covers
- 01
Experimental units and variables
- 02
Population and sample scope
- 03
Descriptive and inferential methods
- 04
Categorical and quantitative data
- 05
Nominal and ordinal scales
- 06
Interval and ratio scales
- 07
Primary and secondary sources
Worked example · free
Classify a delivery file
- 2Identify one row's experimental unit.
- 3Classify all recorded variables.
- 3Separate description from inference.
Key terms
- Experimental Unit
- The object or event on which one set of variable values is observed.
- Population
- Every unit addressed by the statistical question.
- Sample
- The observed subset used to study a population.
- Ordinal Data
- Categories with a meaningful order but no established equal spacing.
- Ratio Data
- Measurements with meaningful differences, ratios and a genuine zero.
Statistical Questions, Data Types and Samples FAQ
Can a number be categorical data?
Yes. Depot codes, product identifiers and satisfaction labels may use digits while remaining categories. Ask whether subtraction or ratios have a defensible interpretation. If code four is not twice code two in the real setting, the digits are labels rather than measured quantities.
Is a complete branch roster a sample or population?
It is the population for a question about that branch and a sample for a claim about a wider company or industry. The target question determines scope. Completeness inside one boundary does not justify inference beyond that boundary without a representativeness argument.
Why does the measurement scale matter later?
The scale determines which summaries and displays preserve meaning. Nominal values support frequencies, ordinal values support ranked comparisons, interval values support differences and ratio values also support ratios. Choosing a mean or model before checking the scale can create precise arithmetic for an invalid comparison.
Exam move
Take ten columns from a business spreadsheet and write the experimental unit, variable type and target population for each. For any coded column, explain whether the digits measure quantity or only name categories. Then choose one sample and write the exact inference it is intended to support, followed by one operating change that could make the sample unrepresentative.
Repeat the exercise after changing the target question from one branch to the whole company; note which dataset changes from population to sample. For each ordinal field, state why rank is meaningful but equal spacing is not established. For each ratio field, explain the real zero and one defensible ratio. Finally, build a five-line opening for a fresh case: unit, population, sample, variables and inference.
Add the data source, observation period, missing-value rule and one representativeness threat. Compare this setup with a classmate's before doing any arithmetic, because disagreements at this stage reveal scope errors that a later formula cannot repair.
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