Week 2 — categorical data

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: How compute relative frequency?
• Procedure: Tally each category. Total n is sum of counts. Relative freq = count/n.
• Variations / traps: Watch for: Percents not summing to 100 due to rounding.

Formula chain (compressed)

frequency table → relative freq = count/n → bar/pie for categories.

1. Frequency — count per category — raw tallies
2. Relative frequency — count / total — proportions sum to 1
3. Mode — most frequent category — categorical centre
4. Bar chart — height = count or % — compare categories
5. Missing category — include "other" or NA — complete sample space

Deep study

Statistics I · Week 2 — Categorical data

Week map

Frequency notation

• Frequency $f$ → count in category → 23 students chose tea.
• Relative frequency → $f / n$ → proportion of whole → 0.23 if $n=100$.
• Percent → relative × 100 → 23%.
• Complement → all categories not A → if A is 30%, complement is 70%.

• Rel freq: 0.40, 0.35, 0.25
• Percents: 40%, 35%, 25%

Charts

Bar chart

• Categories on axis (nominal or ordinal).
• Bar height = count or percent.
• Good for compare across categories.

Pie chart

• Wedges show part-whole.
• Works for few categories; weak for many thin slices.
• Angles proportional to relative frequency.

Pattern families

Easy — Build frequency table

• Tally categories from raw list.
• Compute $n$ as sum of counts.
• Relative freq = count/$n$.

Medium — Chart choice and read

• Pick bar vs pie from question goal.
• Read missing count from percent and $n$: count = percent/100 × $n$.
• Compare two categories via difference in counts or percents.

Hard — Rounding and complements

• Percents sum to 99% or 101% due to rounding — know largest category still identifiable often.
• Given two category percents, find third when three categories total 100%.
• Two-way categorical preview: row percent vs overall percent (setup for week 4).

Worked mini-examples

Traps

• Confusing frequency with relative frequency.
• Pie chart with dozens of categories.
• Percents not summing to 100 — rounding, not always error.
• Bar chart ordered as if ordinal when nominal — order arbitrary unless by count.
• Using pie when categories are not parts of one group total.

Diagnostic (try yourself)

1. Raw: [R,R,B,G,R,B,G,G,R] — build frequency table and $n$.
2. $n=80$, counts A=32, B=20, C=28. Find relative frequencies and percents.
3. In a survey, 35% preferred online and 45% preferred hybrid. The only other option is in-person. What percent chose in-person?
4. $n=200$, 12.5% chose “other”. How many cases?
5. When would a bar chart be better than a pie chart for the same categorical data? One sentence.

ChatGPT prep archive

• Chatty reference archive

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

Core concepts

• Frequency: count per category.
• Relative frequency: proportion or percent of total; sums to 1 (or 100%).
• Bar chart: categories on axis; heights show counts or percents.
• Pie chart: wedges show parts of whole—meaningful for few categories.

Notation & vocabulary

Pattern families

Easy — Frequency table

Medium — Choose chart

Hard — Missing category

Drill these on the pattern atlas — filter to week 2.

Traps

• Percents not summing to 100 due to rounding.
• Bar chart with ordered nominal when order arbitrary.
• Pie chart for unrelated categories not one whole.
• Confusing frequency with relative frequency.

Retrieval prompts

1. How compute relative frequency?
2. When bar vs pie?
3. What must pie wedges sum to?

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 2.
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