📊 Learn Distributions & Percentiles

📖 Learn Concepts
🧮 Calculate Percentiles
📈 Visualize Distribution
✅ Practice

What is a Distribution?

A distribution shows how data values are spread out or arranged. It tells us which values are common and which are rare.

Example: Imagine you recorded the heights (in inches) of 20 students:
65 67 68 70 70 71 72 72 73 74 74 74 75 76 76 77 78 79 80 82

The distribution shows that most students are between 72-76 inches tall, with fewer students at the extremes.

Why Distributions Matter

Distributions help us understand:

What are Percentiles?

A percentile tells you what percentage of the data falls below a certain value. It's a way to understand where a specific value ranks within the dataset.

The Nth percentile means that N% of the data falls below that value, and (100-N)% falls above it.

Common Percentiles

20th Percentile (P20): 20% of the data is below this value, 80% is above it

50th Percentile (Median or P50): The middle value - 50% below, 50% above

80th Percentile (P80): 80% of the data is below this value, 20% is above it

Real-world example: If you scored in the 80th percentile on a test, it means you did better than 80% of the people who took the test!

How to Calculate Percentiles

Step-by-Step Process:

Step 1: Sort the data

Arrange all values from smallest to largest.

Step 2: Calculate the position
Position = (Percentile / 100) × (N + 1)
where N = number of values
Step 3: Find the value
  • If the position is a whole number, use that value at that position
  • If the position has a decimal, interpolate between the two nearest values
Example Calculation:

Data: [10, 20, 30, 40, 50, 60, 70, 80, 90, 100] (10 values)

Finding the 20th percentile:

Position = (20 / 100) × (10 + 1) = 0.2 × 11 = 2.2

Position 2.2 means we interpolate between the 2nd value (20) and 3rd value (30):

P20 = 20 + 0.2 × (30 - 20) = 20 + 2 = 22

🎯 Interactive Practice

Now it's your turn! Enter your own data or use example datasets to practice calculating percentiles and visualizing distributions.

🎓 Summary: What You've Learned

✓ Distributions show how data values are spread out across a range

✓ Percentiles tell you what percentage of data falls below a certain value

✓ To calculate percentiles:

  1. Sort the data from smallest to largest
  2. Calculate position using: (Percentile / 100) × (N + 1)
  3. Find the value at that position (interpolate if needed)

✓ Visualizing distributions with histograms helps you see patterns in your data