Chapter 60: Distribution

Distribution

I’m going to explain it like your favorite teacher — slowly, clearly, with zero scary formulas at the beginning, lots of everyday stories from Hyderabad life, simple pictures you can see in your mind, real numbers you can check yourself, and many concrete examples so you understand why “distribution” is not just a fancy word — it is the shape and story that the data is trying to tell you.

Let’s start with the clearest sentence of the whole lesson:

A distribution is the complete pattern / shape / way in which the values of a variable are spread across all possible values — showing how frequently each value (or range of values) appears.

In simple words: Distribution answers the question: “How are the numbers arranged — are they clumped in the middle, stretched to one side, full of gaps, having extreme outliers, symmetric or lopsided?”

Step 1: Why “Distribution” is the First Thing You Should Look at

Whenever you get any real data (exam marks, delivery times, flat rents, UPI transaction amounts, heights of your friends), the very first intelligent thing to do is:

Look at the distribution before you calculate any average or make any decision.

Because the same average can hide very different realities.

Classic Hyderabad example:

Two tuition centres near your home — both claim “average student score 85% in board exams”

Centre A scores last year: 82, 83, 84, 85, 85, 86, 86, 87, 87, 88 → very tightly clustered around 85 → very consistent teaching

Centre B scores last year: 35, 45, 60, 78, 85, 92, 95, 98, 99, 100 → average also 85, but huge spread — some students fail, some top the class

Same mean, completely different distribution.

If you are choosing a tuition centre for yourself, distribution (consistency) matters far more than the mean alone.

Step 2: The Four Most Important Ways to “See” a Distribution

1. Histogram (the most honest picture)

   → Divide the range of values into bins (e.g., 0–10, 10–20, 20–30…) → Count how many values fall into each bin → Draw bars with height = count

   Example: delivery times from Swiggy last month (in minutes)

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   0 1 2 3 4 5 6 7 8 9 10 11 12

   15–20 min:   ■■■ (3 orders) 20–25 min:   ■■■■■■■■■ (9 orders) 25–30 min:   ■■■■■■■■■■■■■■■■■ (17 orders) 30–35 min:   ■■■■■■■■■■■■■■■■■■■■■ (21 orders) 35–40 min:   ■■■■■■■■■■■■■ (13 orders) 40–45 min:   ■■■■■ (5 orders) 45–50 min:   ■■ (2 orders)

   → You see: most deliveries 25–40 min, peak around 30–35 min, long right tail (few very late deliveries)

2. Box Plot (five-number summary in one picture)

   Shows:

   • Minimum (non-outlier)
   • Q1 (25th percentile)
   • Median (50th percentile)
   • Q3 (75th percentile)
   • Maximum (non-outlier)
   • Outliers (dots far away)

   Example: monthly flat rent in Kukatpally (2026 data)

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   0 1 2 3 4 5 6 7 8 9 10 11 12

   Min       Q1      Median    Q3      Max 12,000   18,000   24,000   35,000   80,000             ┌───────────────┐ ┌───────┐   │               │   ┌───────┐ │       │   │               │   │       │ └───────┘   └───────────────┘   └───────┘             outliers: • • • • (very high-rent luxury flats)

   → Tells you: typical rent ₹18k–₹35k, but some very expensive outliers

3. Density Plot / Smooth Curve (fancy version of histogram)

   Smoothed version — looks like a hill or multiple hills

4. Cumulative Distribution Function (CDF) (less common for beginners)

   Shows “what percentage of values are less than X”

Step 3: The Most Important Shapes of Distributions (With Names & Meaning)

1. Symmetric / Bell-shaped (Normal / Gaussian) → Mean ≈ median ≈ mode → Tails equal on both sides Example: heights of adult men in Hyderabad (most people around 165–175 cm, few very short or very tall)
2. Right-skewed / Positive skew (long tail on the right) → Mean > median > mode → Many small values, few very large values Example: monthly income in Hyderabad — most people earn ₹20k–₹80k, few earn ₹5 lakh+
3. Left-skewed / Negative skew (long tail on the left) → Mean < median < mode → Few very small values, most values large Example: age at death in modern India — very few die young, most die 60–90 years
4. Bimodal / Multimodal (two or more peaks) Example: arrival time of students to college — one peak at 8:30 AM (regular students), another at 10:00 AM (latecomers / second-shift)
5. Uniform (flat) → Every value equally likely Example: lottery numbers (if fair) — each digit 0–9 equally probable

Step 4: Quick Summary Table (Copy This!)

Final Teacher Words

Distribution is the complete shape and story that your data is telling you.

It shows:

• Where most values live (center)
• How much they spread (variability)
• Whether there are clumps or gaps
• Whether there are extreme outliers
• Whether the pattern is symmetric or lopsided

Before you ever calculate a single p-value, build a model, or make a business decision — always look at the distribution first.

In Hyderabad 2026 you meet distributions constantly:

• Delivery times → right-skewed (most 25–40 min, few very late)
• Flat rents → right-skewed (many ₹15k–₹40k, few ₹1 lakh+ luxury)
• Exam marks → often left-skewed in tough subjects (most fail/pass low, few score 95+)
• UPI transaction amounts → heavily right-skewed (many ₹50–₹500, few ₹50,000+)

Distribution is not noise — it is signal. It tells you risk, consistency, fairness, typical behavior, and where the surprises live.

Understood the beauty and importance of distribution now? 🌟

Want to go deeper?

• How to draw a histogram by hand (with small data)?
• Real right-skewed example with Hyderabad flat rents + calculation?
• Why skewness matters when choosing mean vs median?
• Difference between distribution in descriptive vs inferential statistics?

Just tell me — next class is ready! 🚀