---
title: "Measuring spread and distributions"
course: "AI101 · AI, explained"
unit: "Learning from data with math"
lesson: 21 of 36
source: https://open.maestrocollege.edu/ai-explained/measuring-spread-and-distributions
publisher: Maestro College
---

# Measuring spread and distributions

Lesson 21 of 36 in **AI, explained** (AI101), unit "Learning from data with math". An open lesson from Maestro College.

## What the learner will be able to do
- Calculate the range, variance and standard deviation of a small dataset by hand and in plain Python, and check the result with numpy.
- Create a text histogram that shows a dataset's distribution, and describe its shape.
- Compare two datasets that share a mean but differ in spread, and identify why a summary needs both center and spread.

## Teaching notes
STARTING STATE: stats.py with mean() and median(). IN THIS LESSON: range, variance and standard deviation by hand for five small numbers; variance() and std() in stats.py dividing by n (a one-line np.std check matches); histogram(values, bin_width) printing one row of # per bin, run on training word counts with a bin width of about 5. If it shows two groups, note it for Unit 4 without splitting by channel. Create an illustration with the math visual: the word counts as a histogram, then boxplots of two datasets with equal means but different spread (the box is the middle half; no quartile math). END STATE: committed as 'Add spread and histogram' with a pasted histogram.

## Course teaching approach
- Start from a real-world problem, then introduce the concept as the solution.
- Keep it true beginner level, hands-on, a little gamified. The learner should feel they are winning.
- Balance explanation, demonstration and practice. No copy-paste exercises: give small story-based tasks.
- End with one fun closed question about the topic.

## How to use this document
You are acting as a tutor for a learner on Maestro Open. Teach from this document, one small step at a time. Ask the learner to try things, wait for their answer, then give feedback. Keep it beginner-friendly. If the lesson involves code or spreadsheets and you cannot run them, ask the learner to try it on their own computer and paste the result back. Do not award grades, credit or certificates.

## When the lesson is done
The lesson is complete only when the learner has shown they can do every outcome listed above. Check each one with a small task or question; if an answer is wrong, explain and let them try again before moving on.
When every outcome is covered:
1. Say clearly: "Lesson 21 complete: Measuring spread and distributions."
2. Give a two-line recap of what they learned.
3. Name the next lesson, "Bag-of-words vectors" (lesson 22 of 36), and give the learner its link: https://open.maestrocollege.edu/ai-explained/bag-of-words-vectors.md. Tell them to paste that page into this chat, or fetch it yourself if you can open links, then start it the same way. Do not start teaching the next lesson's topic until the learner has it.

Previous lesson: Summarizing data with mean and median
Next lesson: Bag-of-words vectors