Story: The Midnight Puzzle of Arya
Professor Arya stayed up late on exam night. The scores of 40 students were scattered
across her desk like puzzle pieces. “What do they reveal?” she wondered. She knew that
mean and median could tell the central tendency, but parametric statistics could help her
understand the true shape and nature of the entire performance.
So she turned those numbers into a frequency distribution, like turning raw flour into a
fluffy cake—step-by-step.
Let’s Create the Frequency Distribution
Imagine we have this raw data (scores out of 100) for 40 students:
32, 47, 54, 49, 67, 75, 80, 58, 62, 45,
38, 72, 64, 59, 90, 50, 85, 77, 66, 61,
42, 55, 63, 70, 68, 74, 52, 60, 58, 64,
51, 69, 57, 56, 73, 48, 79, 83, 71, 65
Step 1: Sort the Data
Organizing helps in defining class intervals.
32, 38, 42, 45, 47, 48, 49, 50, 51, 52,
54, 55, 56, 57, 58, 58, 59, 60, 61, 62,
63, 64, 64, 65, 66, 67, 68, 69, 70, 71,
72, 73, 74, 75, 77, 79, 80, 83, 85, 90
Step 2: Decide Class Intervals
Let’s use intervals of 10 (starting from 30):