mallory — statistics & probability

Descriptive statistics plus an interval-probability calculator over five distributions.

Via @johnhenry/math's Statistics module (mean, median, standard deviation, five-number summary), plus Distributions.normal/binomial/poisson/studentT/chiSquare for interval probability — every distribution factory exposes the same cdf(x) shape regardless of continuous/discrete, so P(lower ≤ X ≤ upper) is computed identically across all five. An interactive draggable-marker axis (GeoGebra's Probability Calculator UX) is a later extension.

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Descriptive statistics

Data (comma or space separated):

n = 8
mean = 5.0000
median = 4.5000
standard deviation = 2.1381
variance = 4.5714
min / max = 2.0000 / 9.0000
five-number summary = [2.0000, 4.0000, 4.5000, 6.0000, 9.0000]

Smoothing

Uses the data entered in Descriptive statistics above, in entry order.

Kernel: width (odd): show residual (raw − smoothed)

Blue dots = raw data, colored line = smoothed. The first/last 2 point(s) at each edge are trimmed (a "same"-mode convolution boundary sample there averages against zero-padding, not real neighboring data).

Distribution

Distribution:

mean: sd:

P( ≤ X ≤ )

= 0.682689 (CDF(1) = 0.841345, CDF(-1) = 0.158655)

Inference

Test: α:

Uses the data entered in Descriptive statistics above as the (first) sample.

μ₀:

statistic = 6.6144, df = 7.00, p = 0.000300
Reject H₀ at α = 0.05 (p = 0.0003 < 0.05)