Unit 2 · 1.2

Histograms, polygons, ogives

Bars touch at boundaries; polygon at midpoints; ogive at upper boundaries up to n

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Rule cards

Bars touch; the x-axis shows class boundaries; bar height = frequency.

Traps

Centred narrow bars on the midpoints with gaps.
draw separate bars like a bar chart
✓ bars touch and run boundary to boundary
Read the bar next to the one asked about.
read the class to the right of the target
✓ find the class on the x-axis first, then go straight up
Picked the last class as 'the most'.
'which group has the most?' → rightmost bar
✓ most = the TALLEST bar; no bar = 0

Plot a dot at each class MIDPOINT at height f, join with lines, and start and end on the axis (0) one class before the first and after the last.

Traps

Left the polygon floating at both ends.
start at the first midpoint's height
✓ add a 0 point one class before the first and one class after the last
Plotted the dots at boundaries.
dots at 464.5, 473.5, …
✓ dots at midpoints: 469, 478, …

Plot cumulative frequency at each UPPER boundary; start at 0 at the first lower boundary; climb to n; never go down.

Make a cumulative column: each f added to everything above it.
Check the last total equals n.
Plot (first lower boundary, 0), then (each upper boundary, cumulative).
The curve never goes down. (The key's drawn glucose ogive misses this — see Key errors.)

Traps

Plotted the plain frequencies.
2, 1, 5, 12, … → a line that goes up and down
✓ running totals 2, 3, 8, 20, 38, 44, 49, 50
Plotted at midpoints.
x = 62, 67, 72, …
✓ x = upper boundaries 64.5, 69.5, 74.5, …
Plotted each total at the class's LOWER boundary.
(59.5, 2), (64.5, 3) …
✓ start at (59.5, 0) and end at (99.5, 50)