Lesson 5
Mean, median, variance, and standard deviation
Big question
How can we describe the center and spread of a variable?
Lesson progress
Complete checkpoints as you learn
Learning objectives
- Explain mean, median, variance, and standard deviation in plain language.
- Use mean correctly in an interpretation.
- Connect the lesson idea to a formula, graph, Python result, or real example.
Simple explanation
The mean and median describe a typical value. Variance and standard deviation describe how spread out the values are. Together, they help us understand a dataset before estimating any model.
Key terms
- Mean
- The arithmetic average.
- Median
- The middle value after sorting the data.
- Variance
- The average squared distance from the mean.
- Standard deviation
- The square root of variance, measured in the original units.
Sample mean
Example
For wages 18, 22, and 30, the mean is 70 / 3 = 23.33, while the median is 22.
Summary statistics
1import pandas as pd2 3wages = pd.Series([18, 22, 30])4print(wages.mean())5print(wages.median())6print(wages.std())Checkpoint activity
Pause and explain this lesson's main idea in your own words before moving forward.
Try it yourself
Write one plain-English sentence explaining the main idea from this lesson.
Common mistakes
Check these before you move on.
A regression coefficient describes a pattern unless the assumptions or research design support a causal interpretation.
Quick quiz
Which statistic is the middle value after sorting?
Key takeaway
Always summarize center and spread before trying to explain patterns.