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Data Types and Scales of Measurement

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Data Types and Scales of Measurement

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Data Types and Scales of Measurement

🎯 Learning Objectives

After completing this topic, you will be able to:

Distinguish between categorical (qualitative) and numerical (quantitative) data
Recognize the four scales of measurement: nominal, ordinal, interval, ratio
Determine which scale a given variable falls into
Explain why the scale of measurement determines what statistical operations are valid
Convert between data types where appropriate

📋 Prerequisites

Introduction to Statistics (00-intro-statistics) — understand population vs. sample
Basic arithmetic and counting from high school
No prior statistics knowledge needed

📖 Core Content

2.1 Intuition: Not All Data Is the Same

Imagine you're describing your classmates. You might say:

"Rahul has brown eyes" (a category)
"Priya is tall" (a category with ordering)
"The temperature today is 32°C" (a number)
"Ananya scored 85 out of 100" (a number with a true zero) Each of these is a different type of data. The type determines what you can do with it:
Can you compute an average of eye colors? No — that doesn't make sense.
Can you compute an average of test scores? Yes — that's meaningful.
Can you say 40°C is "twice as hot" as 20°C? Actually, no — we'll see why. The type of data you have dictates the type of statistical analysis you can perform. This isn't a minor detail — using the wrong analysis for a data type is one of the most common mistakes in statistics.

🔑 Key Insight: Before you do ANY statistics, ask: "What type of data am I working with?" The answer determines everything else.

2.2 The Big Divide: Categorical vs. Numerical

At the highest level, data splits into two major categories: (Diagram)

Categorical (Qualitative) Data

Categorical data represents categories or groups. The values are labels that place each observation into a group.

Examples: Gender (Male/Female/Other), blood type (A/B/AB/O), country of residence, favorite color, yes/no responses
Can you do arithmetic? No. Adding, subtracting, or averaging categories is meaningless.
What CAN you do? Count how many observations fall into each category, compute percentages, find the mode (most common category)

Numerical (Quantitative) Data

Numerical data represents amounts or measurements. The values are numbers where arithmetic makes sense.

Examples: Age in years, height in cm, number of siblings, temperature in Celsius, test score
Can you do arithmetic? Yes (with some caveats based on the scale)
What CAN you do? Compute mean, median, standard deviation, correlation, etc.

Numerical → Discrete vs. Continuous

Numerical data further splits into two types:

Type	Definition	Examples	Can it be 2.5?
Discrete	Can only take specific, separate values (usually whole numbers)	Number of children, number of cars, roll of a die	No — you can't have 2.5 children
Continuous	Can take any value within a range	Height, weight, time, temperature	Yes — height can be 170.5 cm

Memory trick: Discrete = Distinct, separate values. Continuous = Continuous range, no gaps.

2.3 The Four Scales of Measurement

The psychologist Stanley Smith Stevens introduced four scales of measurement that refine how we think about data types. These scales tell us what mathematical operations are legitimate.

2.3.1 Nominal Scale

Intuition: "Nominal" comes from the Latin nomen (name). These are just names or labels — no ordering, no ranking. Definition: A scale where data is categorized into distinct groups with no order or rank. Each group is mutually exclusive. Characteristics:

✅ Categories are distinct and non-overlapping
✅ Can count frequencies and find the mode
❌ Cannot compute mean, median, or standard deviation
❌ No ordering (one category is not "greater" or "lesser" than another)
❌ No arithmetic allowed Examples:
Gender: {Male, Female, Other}
Blood type: {A, B, AB, O}
Country of birth: {India, USA, UK, ...} -宗教信仰 (Color): {Red, Blue, Green}
Yes/No responses Valid operations: Count, percentage, mode, chi-square test. What's NOT valid: "Average blood type = 1.5" — nonsense.

2.3.2 Ordinal Scale

Intuition: "Ordinal" comes from "order." Now categories have a natural sequence, but the gaps between them aren't necessarily equal. Definition: A scale where categories have a meaningful order, but the differences between categories are not quantifiable or consistent. Characteristics:

✅ Categories have a natural order
✅ Can find the median and mode
✅ Can say "A > B" or "A < B"
❌ Cannot say "A is twice B" — differences aren't meaningful
❌ Cannot compute the mean Examples:
Education level: {High School < Bachelor's < Master's < PhD} — The gap between High School and Bachelor's may not equal the gap between Master's and PhD
Movie ratings: {★, ★★, ★★★, ★★★★, ★★★★★} — We know 4 stars is better than 2, but is ★★★ exactly 1.5× better than ★★? No.
Survey responses: {Strongly Disagree < Disagree < Neutral < Agree < Strongly Agree}
Economic class: {Low < Middle < High} Valid operations: Count, median, mode, percentiles, rank correlation. What's NOT valid: "Average satisfaction is 2.7" — implies equal intervals where they may not exist.

Everyday analogy: A race result (1st, 2nd, 3rd) tells you who finished before whom, but not how much time separated them. The 1st-place runner might have won by 10 seconds or 10 minutes — ordinal data preserves only the order.

2.3.3 Interval Scale

Intuition: Now we have actual numbers with equal intervals, but no true zero point. Zero is arbitrary — it doesn't mean "none." Definition: A scale where the difference between any two adjacent values is the same (equal intervals), but there is no meaningful zero point. Characteristics:

✅ Equal intervals between values — differences are meaningful
✅ Can compute mean, median, mode, standard deviation
✅ Can say "the difference between A and B is 10 units"
❌ Cannot say "A is twice B" — ratios aren't meaningful
❌ Zero is arbitrary (not "absence" of the property) Examples:
Temperature in Celsius: 20°C is not "twice as hot" as 10°C because 0°C doesn't mean "no heat" (0°C is just the freezing point of water, an arbitrary reference). 20°C has 10 more degrees of heat than 10°C, which has the same difference as 30°C vs 20°C.
IQ scores: A person with IQ 140 is not "twice as smart" as someone with IQ 70. But the 30-point gap between 100 and 130 has the same meaning as the gap between 70 and 100.
Calendar years: The year 2000 CE is not "twice as late" as 1000 CE. But the gap between 1900 and 2000 (100 years) equals the gap between 2000 and 2100. Valid operations: Mean, median, standard deviation, correlation, t-tests, ANOVA. What's NOT valid: "40°C is twice as hot as 20°C" — wrong, because 0°C is not a true zero.

2.3.4 Ratio Scale

Intuition: The "gold standard" — everything interval has, plus a meaningful zero point. Zero means "none of this thing." Definition: A scale with equal intervals AND a true zero point that indicates the absence of the measured property. Characteristics:

✅ All characteristics of interval scale
✅ True, meaningful zero
✅ CAN say "A is twice B" — ratios are meaningful
✅ All arithmetic operations are valid Examples:
Height: 0 cm means no height. A person 180 cm tall is twice as tall as a 90 cm child.
Weight: 0 kg means no weight. 80 kg is twice as heavy as 40 kg.
Income: ₹0 means no income. ₹60,000 is twice ₹30,000.
Time spent: 0 seconds means no time. 10 minutes is twice 5 minutes.
Number of children: 0 means no children. 4 is twice 2. Valid operations: ALL — mean, median, mode, standard deviation, ratios, coefficients of variation, multiplication, division. What IS valid: "She earns twice as much as him" — because 0 income is a true absence.

2.4 Comparison Table: The Four Scales

Feature	Nominal	Ordinal	Interval	Ratio
Categories distinct?	✅ Yes	✅ Yes	✅ Yes	✅ Yes
Categories ordered?	❌ No	✅ Yes	✅ Yes	✅ Yes
Equal intervals?	❌ No	❌ No	✅ Yes	✅ Yes
True zero?	❌ No	❌ No	❌ No	✅ Yes
Can compute...
...counts/frequencies?	✅	✅	✅	✅
...mode?	✅	✅	✅	✅
...median?	❌	✅	✅	✅
...mean?	❌	❌	✅	✅
...standard deviation?	❌	❌	✅	✅
...ratios (X is twice Y)?	❌	❌	❌	✅
Examples	Gender, Color	Ratings, Grades	Temp (°C), IQ	Height, Weight, Income

Memory trick: The scales are cumulative. Ratio has everything interval has, which has everything ordinal has, which has everything nominal has. Think of them as layers:

Nominal + order = Ordinal + equal intervals = Interval + true zero = Ratio

2.5 Valid Operations by Scale

Here's a practical guide: what can you compute for each scale?

Operation	Nominal	Ordinal	Interval	Ratio
Frequency / Count	✅	✅	✅	✅
Mode (most common)	✅	✅	✅	✅
Median (middle value)	❌	✅	✅	✅
Mean (average)	❌	❌	✅	✅
Range (max - min)	❌	❌	✅	✅
Standard Deviation	❌	❌	✅	✅
Ratios (2×, 3×)	❌	❌	❌	✅

2.6 Why the Scale Matters — A Detailed Example

Let's see what happens when you ignore the scale of measurement. Bad example: A teacher codes grades as:

A = 4, B = 3, C = 2, D = 1, F = 0 She then computes the "average" grade as 2.7 and concludes the class is between B and C on average. Why this is problematic: Grades are ordinal data. While A > B > C in quality, the gaps between grades aren't necessarily equal. The difference in knowledge between an A and a B student might be much larger than the difference between a C and a D student. By treating the codes as numbers and averaging them, the teacher assumes equal intervals where they don't exist. What she should do: Report the median grade (the middle grade when all are sorted) or the mode (most common grade). These are valid measures for ordinal data. When it's okay: If the teacher can demonstrate that the gaps between grades are roughly equal (e.g., standardized test scores with equal-interval scoring), then the codes become interval data and averaging is legitimate.

2.7 Continuous vs. Discrete — An Important Sub-distinction

Within numerical data, the continuous vs. discrete distinction matters for:

Probability models: Discrete data uses probability mass functions (PMFs); continuous uses probability density functions (PDFs)
Graphing: Discrete data uses bar charts; continuous uses histograms
Counting vs. measuring: Discrete = counting (how many?). Continuous = measuring (how much?)

Property	Discrete	Continuous
Can take value 2.5?	No	Yes
Possible values	Countable (finite or infinite sequence)	Uncountable (any value in an interval)
Example	Number of cars owned	Time spent on website
Graph	Bar chart	Histogram
PMF/PDF	PMF (P(X=x))	PDF (area under curve)

2.8 Worked Examples

Example 1: Identify the Scale (Easy)

Scenario: A survey asks: "How many times have you visited a doctor in the past year?" Responses: 0, 1, 2, 3, 4, 5, or more. Question: What scale of measurement is this? Solution:

Step	Reasoning
1. Can we order the values?	Yes — 3 visits is more than 2, which is more than 1
2. Are the intervals equal?	Yes — the gap between 1 and 2 equals the gap between 2 and 3 (one visit)
3. Is there a true zero?	Yes — 0 visits means no visits, an absence of the event
4. Can we form ratios?	Yes — 4 visits is twice as many as 2 visits
Conclusion	Ratio scale — it has all four properties

Example 2: Identify the Scale (Medium)

Scenario: A restaurant asks customers to rate their dining experience as: Poor, Fair, Good, Very Good, Excellent. Question: What scale is this? Solution:

Step	Reasoning
1. Can we order the values?	Yes — Excellent > Very Good > Good > Fair > Poor
2. Are the intervals equal?	No — the jump from Fair to Good might not equal Good to Very Good
3. Is there a true zero?	No — "Poor" doesn't mean zero experience
4. Can we form ratios?	No — "Very Good" isn't twice "Good"
Conclusion	Ordinal scale — ordered but with unequal intervals

Example 3: Data Type Classification (Harder)

Scenario: For each variable below, classify it as:

Categorical or numerical
If numerical: discrete or continuous
The scale of measurement a) The ZIP code of a person's residence b) The time (in minutes) to complete a puzzle c) A student's year in school (Freshman, Sophomore, Junior, Senior) d) The number of bedrooms in a house Solution: a) ZIP code — Categorical, Nominal
Even though ZIP codes are written as numbers, they're labels for geographic regions
Adding ZIP codes (e.g., 600100 + 400001) is meaningless
There's no order (one ZIP code isn't "greater" than another)
Key trap: Just because data is stored as numbers doesn't make it numerical! b) Time to complete puzzle — Numerical (Continuous), Ratio
Time can take any value (5.3 min, 5.37 min, 5.372 min...) — continuous
Zero time means no time — true zero
10 minutes is twice as long as 5 minutes — ratios are valid c) Year in school — Categorical, Ordinal
Categories have a clear order (Freshman < Sophomore < Junior < Senior)
But the intervals aren't equal — the gap in knowledge between Freshman and Sophomore may differ from Junior to Senior
You can't compute a mean d) Number of bedrooms — Numerical (Discrete), Ratio
Can only be whole numbers (1, 2, 3...) — discrete
0 bedrooms is meaningful (studio apartment) — true zero
4 bedrooms is twice as many as 2 — ratios valid

2.9 Edge Cases & Gotchas

The Case of (Sort-of) Numbers

Some data looks numerical but isn't. This is extremely common. ZIP codes: Stored as numbers, but averaging them is meaningless. They're nominal labels. Student ID numbers: Same story — labels, not measurements. Phone numbers: You wouldn't compute the "average phone number." They're nominal.

Rule of thumb: Ask yourself: "Does it make sense to add two of these? To divide one by another?" If no, it's probably categorical despite looking numerical.

The "Can I Average Likert Scales?" Debate

A Likert scale (e.g., "On a scale of 1-5, how satisfied are you?") is ordinal data. Technically, you shouldn't average it. BUT... in practice, many researchers treat Likert-scale responses as interval data when:

There are 5 or more categories
The response categories are clearly labeled and appear equally spaced
They compute averages all the time The truth: It's a gray area. For this course, we follow the textbook: Likert scales are ordinal, so report medians and modes. In practice, be transparent about your choice.

When Discrete Data Is Treated as Continuous

Sometimes discrete data with many possible values (e.g., annual income in rupees) is treated as continuous for practical purposes. The number of possible values is so large that the "discreteness" doesn't matter. Example: Income can technically be any paisa value (discrete because currency has a smallest unit: 1 paisa = 0.01 rupee). But with billions of possible values, we treat it as continuous.

2.10 Why This Matters

The scale of measurement is not an academic exercise — it has real consequences:

Choosing the wrong analysis: Applying a t-test (which requires interval/ratio data) to nominal data will give nonsense results
Misleading visualizations: Using a bar chart (for categorical) when you should use a histogram (for continuous) obscures the shape of the data
Business decisions: If you treat ordinal satisfaction data as interval and compute a mean of 3.4, you might make decisions based on a number that isn't truly meaningful Every subsequent topic in BSMA1002 builds on this foundation:

Week 2 (Categorical Data): How to summarize nominal/ordinal data
Week 3 (Descriptive Stats): Which measures are valid for which scales
Weeks 9-12 (Probability Distributions): Discrete vs. continuous distributions

📐 Key Formulas / Concepts

Concept	Definition	Valid For	Not Valid For
Nominal	Names/labels, no order	Counts, mode, percentages	Mean, median, ratios
Ordinal	Ordered categories, unequal intervals	Counts, mode, median, percentiles	Mean, standard deviation
Interval	Equal intervals, no true zero	Mean, median, std dev, differences	Ratios ("twice as")
Ratio	Equal intervals, true zero	ALL arithmetic operations	Nothing — this is the fullest scale
Categorical	Groups/labels (qualitative)	Counts, bar charts	Averages, histograms
Numerical Discrete	Countable separate values	Sum, mean, histograms (for many values)	Modeling as continuous (if few values)
Numerical Continuous	Any value in a range	Mean, standard deviation, correlation

⚠️ Common Pitfalls

Pitfall 1: Treating All Numbers as Numerical Data

The mistake: Assuming any data stored as numbers is numerical/quantitative. Why it happens: ZIP codes, student IDs, and year codes look like numbers. Our brains naturally think "number = quantitative." How to catch it: Ask: "Would computing the average of this make sense?" Average ZIP code 560100? That's meaningless. Correct approach: Examine what the number represents. If it's a label or identifier, it's categorical.

Pitfall 2: Treating Ordinal Data as Interval

The mistake: Computing the mean of ordinal data (e.g., average of "Strongly Disagree (1), Disagree (2), Neutral (3), Agree (4), Strongly Agree (5)" = 3.2). Why it happens: The categories are coded as numbers, and computers will happily compute the mean. It feels intuitive. How to catch it: Remember that the gaps between categories might not be equal. Is the jump from Disagree to Neutral the same size as from Agree to Strongly Agree? Probably not. Correct approach: Report the median (the middle category) or mode (most common response) for ordinal data.

Pitfall 3: Claiming Ratio Properties for Interval Data

The mistake: Saying "40°C is twice as hot as 20°C" or "IQ 150 is twice as smart as IQ 75." Why it happens: The numbers look like they support multiplication. If 40 is twice 20, surely... right? How to catch it: Check if zero is meaningful. 0°C doesn't mean "no temperature" — it's just the freezing point of water. IQ 0 doesn't mean "no intelligence." Correct approach: Say "40°C is 20 degrees warmer than 20°C" (interval differences are valid). Never use ratios for interval data.

Pitfall 4: Confusing Discrete and Continuous

The mistake: Treating a discrete variable (like "number of siblings") as continuous. Why it happens: Discrete variables with many possible values (like annual income in rupees) look continuous. How to catch it: Can the value be 2.5? If the smallest meaningful unit is a whole integer, it's discrete. Correct approach: Use bar charts for discrete data (or histograms with careful binning). Use appropriate probability models — discrete distributions for discrete data.

📝 Practice Questions

Q1: Classify the Variable

For each variable, classify it as: (a) categorical or numerical? (b) If numerical, discrete or continuous? (c) Scale of measurement?

i) Marital status (Single, Married, Divorced, Widowed) ii) Distance from home to college (in km) iii) Number of siblings iv) Temperature in Fahrenheit v) Letter grade (A, B, C, D, F)
<details> Solution

Variable	Cat/Num	Discrete/Continuous	Scale
i) Marital status	Categorical	—	Nominal
ii) Distance (km)	Numerical	Continuous	Ratio
iii) Number of siblings	Numerical	Discrete	Ratio
iv) Temp (°F)	Numerical	Continuous	Interval
v) Letter grade	Categorical	—	Ordinal

Reasoning for each:

Marital status: Labels with no order — nominal.

Distance: Can be 2.5 km, 2.55 km, etc. — continuous. True zero — ratio.

Siblings: Whole numbers only (0, 1, 2...). 0 means none — ratio.

Temp in °F: Equal intervals but 0°F doesn't mean no heat (it's just really cold) — interval.

Letter grade: Ordered but unequal gaps — ordinal.

</details> > **Q2: Valid Operations** > > For a variable measured on a ratio scale (e.g., annual income in ₹), which of the following are valid? > > a) Mean income b) "Person A earns twice as much as Person B" c) Median income d) Standard deviation of income e) Mode income > > <details> Solution > > **All are valid.** Ratio scale supports EVERY statistical operation. > > - **Mean:** ✅ — sum of incomes divided by count > - **Ratio (twice):** ✅ — because ₹0 is true zero (no income) > - **Median:** ✅ — ordering is meaningful > - **Standard deviation:** ✅ — equal intervals make spread measures valid > - **Mode:** ✅ — always valid for any data type </details> > **Q3: Challenging Classification** > > A website ranks products as "1 star" to "5 stars" based on customer reviews. The star rating is the **average** of all customer ratings for that product (each customer gives 1-5). What scale is the product's displayed star rating? > > <details> Solution > > **Answer:** It depends on how you interpret it! > > **Strict interpretation:** The displayed star rating (e.g., 4.2 stars) is an **average** of individual ratings. Since individual ratings (1-5) are ordinal, the average could be argued as ordinal. > > **Practical interpretation:** Many researchers treat averaged star ratings as **interval** data because: > > - The underlying values (1-5) are treated as having equal intervals > - The average creates a continuous-like measure (4.2, 3.7, etc.) > - Differences like "4.2 is 0.5 stars higher than 3.7" are meaningful > > **IITM course answer:** Technically ordinal. But in practice, treat with caution. > > **Key insight:** This is a gray area in statistics. Being aware of the debate matters more than picking the "right" answer. </details> > **Q4: Real-World Scenario** > > A hospital records the following data for each patient: > >

Variable	Example Value
Patient ID	P12345
Blood type	A+
Age (years)	45
Body temperature (°C)	37.2
Pain level (0-10 scale)	6
Number of previous visits	3

Classify each variable's scale of measurement.
<details> Solution

Variable	Scale	Reasoning
Patient ID	Nominal	Just a label — no order, no arithmetic
Blood type	Nominal	Categories with no order
Age (years)	Ratio	True zero (0 years = newborn), equal intervals, ratios valid (60 is twice 30)
Body temp (°C)	Interval	Equal intervals, but 0°C is not "no temperature"
Pain level (0-10)	Ordinal	Ordered categories, but is the gap between 2 and 3 equal to 6 and 7? Unclear
Previous visits	Ratio (Discrete)	True zero, countable, ratios valid

</details> > **Q5: Data Conversion** > > A researcher collects income data as ranges (lab categories): > > - "Less than ₹20,000" > - "₹20,000 - ₹40,000" > - "₹40,001 - ₹60,000" > - "More than ₹60,000" > > What scale is this? What information is lost by converting to categories? > > <details> Solution > > **Answer:** This is **ordinal** data (ordered categories). > > **What's preserved:** > > - The ordering (higher income brackets are genuinely higher) > - We can find the **median** income bracket > > **What's lost:** > > - Exact income values — we don't know if someone in "₹20,000 - ₹40,000" earns ₹22,000 or ₹38,000 > - The ability to compute a meaningful **mean** — we could approximate it using category midpoints, but it would be rough > - The ability to compute **standard deviation** precisely > - The ability to form **ratios** (we can't say "Person A earns twice as much") > - We've downgraded from **ratio** scale (exact income) to **ordinal** scale > > **Lesson:** Whenever possible, collect the rawest form of data. You can always aggregate later, but you can't recover lost detail. </details> > **Q6: Multiple Choice** > > Which of the following is NOT valid for ordinal data? > > a) Mode b) Median c) Mean d) Percentiles > > <details> Solution > > **Answer:** c) Mean > > **Reasoning:** > > - **Mode** (most common category): ✅ Valid — just count frequencies > - **Median** (middle category when sorted): ✅ Valid — ordering is meaningful > - **Mean:** ❌ Invalid — requires equal intervals, which ordinal data lacks > - **Percentiles** (e.g., 25th, 75th): ✅ Valid — based on ordering > > The mean assumes that the distance between values is consistent. With ordinal data, we can't guarantee that. </details> > **Q7: Coding Challenge (Python)** > > You have a dataset with a column "rating" that contains values "Poor", "Fair", "Good", "Very Good", "Excellent". You need to convert this to numbers for analysis. What's the correct approach? > > <details> Solution > > **Answer:** Create an ordered mapping, but DON'T compute the mean of the mapped values for your primary analysis. > > ```python > # Correct mapping > rating_mapping = { > "Poor": 1, > "Fair": 2, > "Good": 3, > "Very Good": 4, > "Excellent": 5 > } > > # Convert to numeric > df['rating_num'] = df['rating'].map(rating_mapping) > > # Valid: report mode and median > mode_rating = df['rating'].mode()[0] > median_rating_num = df['rating_num'].median() > > # Problematic: computing mean > mean_rating = df['rating_num'].mean() # Use with caution — technically ordinal > ``` > > **Interpretation:** Report the median rating. If you compute the mean (many researchers do), acknowledge the assumption that intervals are equal. </details> > **Q8: Application Question** > > A company measures customer satisfaction on a 1-10 scale. The mean satisfaction score is 7.3. A junior analyst claims: "Customers are 7.3 times more satisfied than unsatisfied." What's wrong with this statement? > > <details> Solution > > **Problems with the statement:** > > 1. **Scale confusion:** A satisfaction score of 1-10 is **ordinal** (or at best interval, debatable). The analyst is treating it as **ratio**. > > 2. **Ratio misinterpretation:** "7.3 times more satisfied" implies that 0 is "no satisfaction" and that 7.3 has a meaningful ratio to 1. But 0 might not represent "no satisfaction" — it's just the lowest rating. > > 3. **Mean of ordinal data:** Computing the mean of a 1-10 satisfaction score assumes equal intervals (that each step from 1→2 is the same as 7→8). This may not be true — people's perception of satisfaction isn't necessarily linear. > > > **Correct interpretation:** "The average satisfaction rating is 7.3 out of 10, which is above the midpoint of 5.5." This describes **where** the average falls without making ratio claims. </details> * * * ## 🔗 Cross-References - **Next topic:** [Categorical Data — Frequency Tables and Charts](/notes/01-foundation-bsma1002-stats-1-week02-02-categorical-frequency) — applying these concepts to real categorical data - **BSMA1001-maths-1**: Sets — categories are just subsets of a universal set - **BSMA1002 Week 3**: Descriptive statistics — the mean, median, and mode, and why their applicability depends on the scale - **BSMA1004 (Stats 2)**: More advanced modeling where data type determines model selection - **External**: [IITM BS Stats 1 — Week 1](https://study.iitm.ac.in/) [Join Discord](https://discord.gg/gE2m4Qrdqv) [Previous**Intro to Statistics**](/notes/01-foundation-bsma1002-stats-1-week01-00-intro-statistics)[Next**Sampling Methods**](/notes/01-foundation-bsma1002-stats-1-week01-00a-sampling-methods)