Data, Averages & Graphs
Grades 5+ Statistics Science
Data is just numbers with a story attached. The skill isn't calculating averages — it's knowing which average tells the truth and spotting when a chart is trying to sell you something.
Three kinds of "average"
data: 2, 3, 3, 5, 7, 9, 100
mean = (2+3+3+5+7+9+100) ÷ 7 = 18.4
median = middle value = 5
mode = most frequent = 3
- Mean — the fair-share average. Best when data is evenly spread; dragged hard by one huge outlier (that 100 pulled the mean to 18 when most values are under 10).
- Median — the middle. Immune to outliers; that's why "median house price" is honest and "average house price" can mislead.
- Mode — the most common. Best for categories and peaks.
Watch out — the outlier trick
"Average salary at Company X is $200,000" can be true while every
ordinary employee earns $45,000 — if the CEO earns millions.
Ask which average they mean. Mean hides skew; median reveals it.
How graphs lie (politely)
- Truncated axis: a bar chart that starts at 50 instead of 0 makes 52 look double 51. Check where the axis begins.
- Stretched axes: the same data looks dramatic or flat depending on how the axes are squeezed.
- Missing labels: "growth" of what? Over what period? An unlabeled chart is a magic trick.
- Cherry-picked range: start the timeline after the bad year and every graph looks like progress.
From counting to a science
Modern data science — including the algorithms that rank this site in search results — grew directly out of descriptive statistics. Two landmark reads:
- Donoho, D. (2017). 50 years of data science. Journal of Computational and Graphical Statistics, 26(4), 745–766. doi:10.1080/10618600.2017.1384734 · arXiv:1512.04886 — a Fields-level statistician on what "data science" actually is.
- Bryan, K., & Leise, T. (2006). The $25,000,000,000 eigenvector: the linear algebra behind Google. SIAM Review, 48(3), 569–581. doi:10.1137/050623280 — the SIAM classic showing how ranking web pages is literally a giant averaging problem.
Try it yourself:
- Mean vs median of 4, 5, 6, 7, 48 (mean 14, median 6)
- A chart's y-axis runs 95–100 — suspicious? (yes — check what difference it's amplifying)
- Most common test score: 70,70,80,80,80,90 (mode: 80)
Related: measurement & error · estimation · percents.