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Module 1 · Descriptive Statistics · DS-2
Last class, Maya finished her CEGEP sleep survey. Today her newsroom needs it turned into charts — and needs her to catch the ones that lie before they go to print.
Live session · join with code OTTO-DS2 · ottolearn.org/join
Same rules as last class: vote before I explain, every poll is anonymous, and changing your mind after discussion is the goal.
Today · Maya's data desk
Frequency distributions
Histograms
Bar charts
Other graph types
Choosing the right graph
Misleading graphs
Each step is a real call Maya has to make at her newsroom desk — and a poll you'll answer first.
Recall · last class · 45 seconds
Warm-up · 60 seconds · anonymous
Hold that suspicion. By the end you'll name exactly what was done — and how to catch it every time.
Core concept 1 · C1
Even a sample of Maya's survey responses — just 20 numbers — is hard to read at a glance. The fix: group the data into classes — equal-width bins. Rule of thumb: aim for about 5 classes; width ≈ range ÷ classes, rounded up to something tidy. Her 20 responses span 4.2–8.4 h — a range of 4.2 h, so \(4.2 \div 5 = 0.84\) → round up to a clean 1 h. That's exactly the classes below. A frequency distribution then counts each class three ways:
How many observations fall in each class. Just a count: \(f\).
\(f\)The count as a share of the whole: \(f / n\). Lets you compare groups of different sizes.
\(f/n\)A running total as you move up the classes — “how many are at or below this point?”
running \(\Sigma\)One table, three lenses: how many, what share, and how many so far.
I do · watch the table build
Full support — watch the table build from raw data, one class at a time.
Here are 20 of Maya's survey responses — hours slept the night before. Watch the whole table build — one class, then one column at a time. Click through it with me.
We do · you fill the last cell
Support fades — the table is set up; you supply the last cumulative cell.
A class of \(n = 50\) students. The first three classes have frequencies 8, 15, 12.
What is the cumulative frequency after class 3?
Practice · C1 · frequency reasoning
On your own now — fresh data, every count yours. Re-roll as many as the room needs.
Core concept 2 · C2
For quantitative data. Bars touch — the x-axis is a continuous number line, so there's no gap between classes.
bars touchThe touching bars say “these values flow into each other.” That's the visual signature of measured, continuous data.
gapsBars touch = continuum. Remember that — it's how you'll tell a histogram from a bar chart in 10 minutes.
I do · watch the table become a picture
Full support — watch the histogram grow from the same 20 readings.
Same 20 sleep readings, table already tallied. Now we draw it — one class, one bar at a time. Click through it with me.
Raw sleep hours (n = 20)
Notice: the choices we made back at the table (how many classes, how wide) decide the shape you see here. Same data, different impression — hold that thought.
We do · you supply the last step
Support fades — the bins are drawn; you supply the last bar's height.
28 exam scores, min 41, max 98.
What class width should we use (round up to a tidy number)?
Practice · C2 · read a histogram
On your own now — fresh distributions to read. Re-roll as many as the room needs.
See it · C2
Predict first: as you make the bins wider, does the distribution look smoother or spikier?
| Class | f | fr | cf | cfr |
|---|
Quick check · C2 · 45 seconds
Core concept 3 · C3
Categories are separate — nothing exists “between” two bars, so we draw space between them.
No natural order for categories, so you may sort by size for readability — but disclose it (remember Georgia).
Is the x-axis a number line? Yes → histogram (touching). No → bar chart (gaps).
Touching vs gaps isn't decoration — it tells the reader whether the x-axis is numbers or names.
Core concept 4 · C4 · the rest of the toolkit
Part-to-whole, ≤5 slices. A bar chart is usually easier to compare.
Small data sets — keeps the raw values visible while showing the shape.
Two quantitative variables — reveals relationships.
A value over time. A non-zero y-axis can be legitimate here — if disclosed.
Spot the flaw · C4 · tap the wrong line
Core concept 5 · C5
One variable → distribution graphs. Two → relationship graphs (scatter, time-series).
This is the DS-1 question. Qualitative → bar chart. Quantitative → histogram.
Part-to-whole with ≤5 categories? A pie can work. Trend over time? Time-series.
The very first fork is variable type — exactly what you classified last class. Your turn:
We do · you make the call
A researcher records the blood type (A, B, AB, O) of 500 donors.
Which graph, and why?
Which tool applies? · mixes in DS-1
Practice · C5 · which graph?
C6 · Predict first · ConcepTest · vote → discuss → re-vote
Core concept 6 · C6 · name the tricks
Y-axis starts above zero, so small differences look enormous. Bar charts should start at 0.
Sorting an x-axis that should be time (or any natural order) to fake a trend. ← what Georgia did.
Doubling a value but scaling an icon's width AND height quadruples the area the eye sees.
Each trick keeps the numbers accurate and corrupts the impression. That's why “the data is real” is no defence.
See it · C6
Predict first: as you raise where the y-axis starts, what happens to a 3-point difference between two bars?
This is the Georgia COVID chart's cousin. The fix in both cases is the same: put the axis back where it belongs and the real story reappears.
Practice · C6 · spot the trick
Production · partners · one sentence
Exit ticket · muddiest point · anonymous
Wrap
Summarize — frequency tables: count, share, running total.
Match — the graph to the variable; type decides the tool.
Audit the axis — “the numbers are real” is never the whole story.
Next class: from one variable to summarizing the centre and spread with numbers.
Chart examples inspired by real incidents (Georgia DPH, April 2020) — illustrative, not cited studies.