A short introduction to density plots

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*Distributions*

Who made more at age 25, millenials or baby boomers?

*Initial approach: Compare summary statistics*

25 year-old boomers

$40k

$50k$0k

$42k

$50k$0k

$10k

$50k

$13k

$50k

$27k

$50k

$40k

$42k

$10k

$13k

$27k

25 year-old millennials

$80k

$50k

$100k

$13k

$50k

$40k

$32k

$50k

$40k

$16k

$50k

$40k

$0k

$50k

$40k

$80k

$13k

$32k

$16k

$0k

Median: $50k Mean: $26.4k Mean: $50k < > = Mean: $28.2k Mean: $50k Mean: $52k Median: $50k Median: $40k

mean(x) =

^{∑x}⁄_{n}$ $ $ $ $ $ $ $ $ $

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

Median ≈ 50th percentile

$10k

$20k

$40k

$80k

$100k

Half the data Median Half the data

Trimean, Winsorized mean, Geometric median, Interquartile mean, Midrange, Truncated mean, Weighted arithmetic mean, Mode, Geometric mean, Tukey median, Midhinge, Harmonic mean, Root mean square, Simplicial depth, Winsorized mean, Trimean, Geometric median, Interquartile mean, Midrange, Truncated mean, Weighted arithmetic mean, Mode, Geometric mean, Tukey median, Midhinge, Harmonic mean, Root mean square, Simplicial depth, Trimean, Winsorized mean, Geometric median, Interquartile mean, Midrange, Truncated mean, Weighted arithmetic mean, Mode, Geometric mean, Tukey median, Midhinge, Harmonic mean, Root mean square, Trimean, Winsorized mean, Geometric median, Interquartile mean, Midrange, Truncated mean, Weighted arithmetic mean, Mode, Geometric mean, Tukey median, Midhinge, Harmonic mean, Root mean square, Simplicial depth, Winsorized mean,

Boomers

Millennials

Area = 0.0000135 × 50,000 × 0.5 ≈ 0.34

Percentiles