Phase 3: Data & Statistical Literacy · ~30 minutes · Python · uv

Distributions — Why Shape Matters

A histogram with a sudden spike at exactly zero usually isn't telling you about zero. It's telling you where the missing data got hidden.

Hiring signal: Looks at a distribution's shape before trusting a single summary statistic about it

What you will learn

Build and read a histogram to see a dataset's shape, not just its average
Distinguish a roughly symmetric (bell-shaped) distribution from a skewed one
Explain why real-world data is often not bell-shaped, and why assuming it is can be consequential
Predict whether mean > median or mean < median from a described skew direction

Introduction

Type: Learn Languages: Python Prerequisites: Lesson 02 (Descriptive Statistics — Center and Spread) Time: ~30 minutes

Objective

Learning objectives

Build and read a histogram to see a dataset's shape, not just its average
Distinguish a roughly symmetric (bell-shaped) distribution from a skewed one
Explain why real-world data is often not bell-shaped, and why assuming it is can be consequential
Predict whether mean > median or mean < median from a described skew direction

What you're building

A script (shape_audit.py) that:

Builds an ASCII histogram (bucket + count, using # characters) of a real dataset of at least 15 numbers that you construct
Correctly identifies, in a printed statement, whether your dataset is roughly symmetric, right-skewed, or left-skewed, based on comparing mean vs. median
Deliberately includes a data-entry bug of your own invention (a suspicious spike at a specific value, not necessarily zero — could be a sentinel value like -1 or 999) that the histogram reveals, and a comment identifying it and computing the statistic both with and without it

A distribution is described as having "a small cluster of very low values and the vast majority of values clustered near the high end" — a left-skewed shape. What's the correct prediction about mean vs. median?

This is the general rule from this lesson's exam-scores predict block, applied to a new description. A tail on the low end pulls the mean toward it more strongly than it pulls the median, because the mean is sensitive to every value's magnitude while the median only cares about position in the sorted order. Left-skewed (tail toward low values) means mean < median; right-skewed (tail toward high values, like the salary example) means mean > median — the direction of the tail directly predicts the direction of this relationship.

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