Week 1 — data & measurement scales

Quiz 2 scope: Weeks 1–8 per IITM May 2026 foundation courses. Source baseline: IITM BS admissions important-dates calendar · May 2026 cycle. Times on assessments are operational conventions — verify hall ticket.

Week map

Classify → Represent → Execute → Trap-check

• Recognize: Ask: Difference categorical vs numerical?
• Procedure: Ask: number or category? If category, order meaningful? Fixed zero? Determines scale and allowed summary.
• Variations / traps: Watch for: Averaging ordinal codes.

Formula chain (compressed)

case → variable → type (categorical/numerical) → scale (nominal…ratio) gates legal summaries.

1. Population vs sample — parameter vs statistic — wording of claim
2. Categorical — labels / categories — mode, bar charts
3. Numerical — counts or measures — mean, spread
4. Scales — nominal < ordinal < interval < ratio — which ops allowed

Deep study

Statistics I · Week 1 — Data types and measurement scales

Week map

Core vocabulary

• Case → one observed unit → one row often → student #42, Tuesday’s weather, one transaction.
• Variable → characteristic recorded per case → column → height, major, rating.
• Value → one observation of a variable for one case → 172 cm, "CS", 4.
• Label → name of variable → not the same as a value.

Type split

Measurement scales

• Nominal → categories, no order → gender codes, zip codes.
• Ordinal → ordered categories → Likert “satisfied”, medal ranks.
• Interval → differences meaningful, no true zero → Celsius temperature.
• Ratio → true zero, ratios meaningful → mass, distance, income.

• Shirt size S,M,L,XL → ordinal (order) but not ratio (L is not “twice” S).
• Year 2024 → interval-like for calendar years (no year 0 in CE) — often taught as not ratio.
• Kelvin → ratio (0 K means no thermal energy).

Valid operations (quick gate)

Pattern families

Easy — Classify variable

• Given description, state categorical vs numerical.
• Pick scale for one variable with reason in one line.
• Identify case count n from table rows.

Medium — Table orientation

• Rows as cases, columns as variables (usual).
• Distinguish variable name from value entry.
• Several variables same cases — joint dataset.

Hard — News headline traps

• ID numbers nominal, not “big number” numerical analysis.
• ZIP code nominal — do not average.
• Percent correct as ratio; letter grades ordinal.

Worked mini-examples

• route_id categorical nominal
• passengers numerical discrete
• on_time categorical nominal (binary)

Traps

• Confusing variable with value (“variable is John”).
• Treating student ID as numerical for correlation.
• Averaging ordinal satisfaction codes blindly.
• Ratio claims on interval scales (twice as hot in °C).
• Binary categorical treated as numerical 0/1 without context — sometimes OK for modeling, but type is still categorical.

Diagnostic (try yourself)

1. Classify each variable as categorical or numerical: (a) number of siblings, (b) favorite fruit, (c) body temperature in °F, (d) race finish position.
2. For “years of education completed”, which scale (nominal/ordinal/interval/ratio) is most appropriate? Brief reason.
3. A spreadsheet has 200 rows and 15 columns of student records. What is n? How many variables?
4. Why is “mode of zip code” silly but “mode of eye color” OK?
5. Give one example variable that is numerical discrete and one numerical continuous.

ChatGPT prep archive

• Chatty reference archive

Archived import for extra depth — complements the notes above, not official IITM material.

Core concepts

• Case: one observed unit (person, day, transaction).
• Variable: characteristic measured on each case; label names it.
• Types: categorical vs numerical; scales: nominal, ordinal, interval, ratio.
• Valid ops: ratio allows all arithmetic; nominal only counts/mode.

Notation & vocabulary

Pattern families

Easy — Classify variable

Medium — Cases vs variables

Hard — Scale traps in news

Drill these on the pattern atlas — filter to week 1.

Traps

• Averaging ordinal codes.
• Treating ID numbers as numerical.
• Confusing variable with value.
• Ratio scale without true zero claimed.

Retrieval prompts

1. Difference categorical vs numerical?
2. Why is Celsius interval not ratio?
3. What is a case in a dataset?

Practice loop

1. Read Deep study (if present) or core concepts once.
2. Recite the formula chain without looking.
3. Open one easy pattern on the interactive atlas for week 1.
4. Attempt without solutions; mark studied after an honest try.
5. Say one trap aloud before closing the tab.

Related

• Full weeks 1–8 prep guide
• Pattern atlas note
• Formula chain desk