Quick check · Weighted mean
Level II · Optional · Open anytime
Applied Descriptive Statistics
A compact applied lab for researchers comparing strategy samples. Move beyond a single average to weighting, robust summaries, group composition, conditional rates, and comparable time windows. Every calculation describes the supplied observations; inference and strategy approval require additional evidence.
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Choose the estimand · Section 1 of 2
Weighted means: whose average are you reporting?
A weighted mean is the sum of value times weight divided by the sum of weights. The weights define the question: equal weights describe a typical row, share-count weights describe a typical share, and notional weights describe a typical dollar of exposure. None is universally the correct average.
For descriptive distributions, use nonnegative weights with a positive total. Signed portfolio exposures are useful in other calculations, but do not form an ordinary probability distribution: a negative observation weight can break cumulative-share interpretation. Also distinguish a fee per order from a fee per dollar before aggregating.
A headline average can change because group values change, because group weights change, or both. Decompose these effects before saying that execution or research quality improved. A shift toward smaller, easier orders can make average cost look better without improving the execution of either order type.
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Keep in mind: Name the unit of observation and the weighting scheme before interpreting an average.
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Quick check · Estimand
A cost report switches from equal-order to notional weighting. How should a lower reported average be interpreted?
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Calculus I & II
Study single-variable calculus with worked steps, visual explorations, and immediate-feedback checks: from limits and derivatives to integrals, series, and approximation error, closing with mental math techniques.
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Applied Descriptive Statistics
Compare research samples using weighted summaries, robust location and scale, within- and between-group dispersion, conditional tables, and consistent time windows.
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Intermediate Python for Research
Build reliable research workflows with explained code examples, revealable output, and interactive checks on NumPy, pandas, timing, validation, and reproducibility.
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