Chapter 47: R Median

1. What the Median Actually Is (Intuitive Explanation)

The median is:

the middle value in a list of numbers after you sort them from smallest to largest.

• If you have an odd number of values → the median is the one right in the center.
• If you have an even number → the median is the average of the two middle values.

Real-life feeling Imagine 7 friends stand in a line ordered by how much they spent on food delivery last month:

₹1,800 – ₹2,900 – ₹3,200 – ₹3,800 – ₹4,100 – ₹4,500 – ₹12,500

→ The median is the 4th person: ₹3,800 Even if one friend ordered a huge party catering for ₹12,500, the median does not move much — it still represents what the typical person spent.

Compare that to the mean: (1800 + 2900 + 3200 + 3800 + 4100 + 4500 + 12500) / 7 ≈ ₹5,114 → The one big order pulled the mean up by more than ₹1,300 — it no longer feels like a “typical” value.

This is why the median is called robust / resistant to outliers.

2. Exact Definition & How to Calculate It by Hand

Step-by-step:

1. Sort the numbers from smallest to largest
2. Find the position of the middle value:
   • If n is odd → position = (n + 1) / 2
   • If n is even → average of positions n/2 and (n/2 + 1)

Examples:

Odd count (7 values) Sorted: 1800, 2900, 3200, 3800, 4100, 4500, 12500 Middle position: (7 + 1)/2 = 4th value → 3800

Even count (6 values) Sorted: 2900, 3200, 3800, 4100, 4500, 12500 Middle positions: 3rd and 4th → (3800 + 4100)/2 = 3950

3. How R Calculates the Median (Hands-on)

2026 golden rule (same as mean): Always write median(x, na.rm = TRUE) unless you intentionally want to know that there are missing values.

4. Real Hyderabad Examples – When Median Wins Big

Example A – Apartment rent in Hyderabad (2026)

→ Real estate portals, government reports, and news articles in India almost always report median rent / house price — never mean — for exactly this reason.

Example B – Delivery time from Swiggy/Zomato (minutes)

→ Food delivery companies usually advertise median delivery time in their reports.

Example C – Exam marks in a large class (skewed left or right)

→ Here median is higher because there are a few low outliers pulling the mean down.

5. When to Choose Median Over Mean (Practical 2026 Guide)

Use median when:

• Data is skewed (right-skewed: income, house price, time-to-delivery, time-to-failure)
• There are outliers or extreme values that are real but not typical
• You want to report what is typical / representative for most people
• Data is ordinal (rankings, Likert scales: 1–5)
• You are reporting to non-technical audience (journalists, managers, general public)

Use mean when:

• Data is symmetric / bell-shaped (no strong skew)
• No extreme outliers (or you already removed/winsorized them)
• You need the value for further calculations (variance, standard deviation, many statistical formulas require the mean)
• You are doing physics / engineering averages (temperature, speed, voltage)

Both together is often best Many real reports say: “Mean = ₹33,110 (skewed by luxury apartments), Median = ₹19,000 (more typical rent)”

6. Your Mini Practice Right Now (Copy → Run & Experiment)

Now try these changes and observe:

1. Add three more very high rides (₹4,800, ₹5,200, ₹6,100) → see mean explode
2. Add ten rides all costing exactly ₹420 → see how median and mode behave
3. Make data left-skewed (many high values, few low) → see mean < median

You just witnessed the core difference with your own numbers.

Clearer now?

Next logical questions?

• Want to learn quartiles, percentiles, IQR next (they are all based on median thinking)?
• See variance & standard deviation (which depend on mean)?
• Compare mean/median in real built-in data sets (iris, mtcars, diamonds)?
• Or jump to first real statistical test involving means (t-test)?

Just tell me — whiteboard is ready! 📊🧮🚀