ST4 · Grouped graphs 1 / Grouped graphs 2 / Shape / H: density / skew Distributions and statistical graphs mind map

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ST4 · Grouped graphs 1 / Grouped graphs 2 / Shape / H: density / skew Distributions and statistical graphs mind map

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Grouped graphs 1

Class boundaries: Boundaries depend on recording precision.
Frequency polygons: Midpoints on x, class frequencies on y.
Equal-width histograms: Touching intervals; equal widths allow frequency heights.
Cumulative frequency: Running totals at upper class boundaries.

Grouped graphs 2

Quartiles from curves: Read quartiles at quarter, half, three-quarter totals.
Box plots: Five-number summary; box covers middle 50%.
Discrete cumulative data: Distinguish discrete exact totals from grouped estimates.

Shape

Positive and negative skew: The longer tail names the skew.
Box-plot evidence: Unequal half-box spreads suggest asymmetry.
Interpret shape: Link concentration and tails to context.

H: density / skew

Higher: Frequency density: Density = frequency ÷ width; area encodes frequency.
Higher: Recover histogram counts: Count = density × width; partial areas are estimates.
Higher: Skew coefficient: Sign from mean minus median; divide by SD.

Connections

Grouped graphs 1 → Grouped graphs 2: Cumulative displays use class boundaries to locate quartiles for a five-number summary.
Shape → H: density / skew: Distribution asymmetry can be judged by tails or summarised using the supplied skew coefficient.