Statistics

Calculate the percentage error between an observed value and a theoretical value.

Returns median of 5 values.

Weighted average rating.

CV = σ/μ.

d = (μ1−μ2)/σ.

k = y/x.

r between two pairs.

MCC = (TP·TN−FP·FN)/√((TP+FP)(TP+FN)(TN+FP)(TN+FN)).

cov for 3 pairs.

D-th decile of 5 values.

Mean of 5 values.

Range of 5 values.

Sum: δz=√(δx²+δy²).

Approx σ from f and midpoints.

IQV = k(N²−Σf²)/(N²(k−1)) (2 cats).

IQR = Q3 − Q1.

Returns min of 5 values.

MAD = Σ|xi−x̄|/n.

Returns mean.

Median of 5 values.

MAD = median(|xi−med|).

(max+min)/2.

Returns max−min of 5.

Most frequent value among 5.

MSE = Σ(yi−ŷi)²/n.

Upper fence = Q3 + 1.5·IQR.

Same as correlation; 3 pairs.

p-th percentile of 5.

PR = (below+0.5·equal)/n·100.

sp=√(((n1−1)s1²+(n2−1)s2²)/(n1+n2−2)).

σ² of 5 values.

Cp = (USL−LSL)/(6σ).

Q-th quartile of 5.

D = 1 − Σ(ni/N)².

max − min.

RSD = σ/μ·100.

RSE = SE/μ·100.

D = 1 − Σ(ni/N)².

Skew ≈ 3(mean−median)/σ.

ρ = 1 − 6Σd²/(n(n²−1)) (3 pairs).

Sample s of 5.

SDI = (x−μ)/σ.

σx̄ = σ/√n.

SE = s/√n.

SS = Σ(xi−x̄)² for 5.

Upper = Q3 + 1.5·IQR.

Sample s² of 5.

|A∪B| = |A|+|B|−|A∩B|.

P(d)=log10(1+1/d).

Mean = α/(α+β).

P(X=k)=C(n,k)p^k(1−p)^(n−k).

Returns IQR for 5 values.

SE = σ/√n.

χ² = Σ (O−E)²/E (2 cells).

Width = ceil(range/classes).

CI = x̄ ± z·σ/√n.

Adds ±0.5 to bound.

Returns mean of 5 values.

Cohen's d = (μ1−μ2)/σ.

68-95-99.7 bounds (returns ±1σ upper).

P(X≤x)=1−e^(−λx).

y = y0·e^(rt).

Bins = ceil(√n).

Sum of frequencies.

P(X=k)=(1−p)^(k−1)·p.

Bin count = ⌈log2(n)+1⌉ (Sturges).

P=C(K,k)C(N−K,n−k)/C(N,n).

Approx z for given p (Beasley-Springer).

Mean = e^(μ+σ²/2).

P(X=k)=C(k−1,r−1)p^r(1−p)^(k−r).

P(X≤x)=Φ((x−μ)/σ).

z=(x̄−μ)/(σ/√n).

Angle = (part/total)·360.

P(X=k)=λ^k·e^(−λ)/k!.

Mean = σ·√(π/2).

rf = freq/total.

SE = √(p(1−p)/n).

Approximate SMp(x) PDF at x (illustrative).

Sum of 5 values.

Mean=(a+b)/2.

UCL = x̄ + 3·σ.

P(X≤x)=1−e^(−(x/λ)^k).

Δx = (max−min)/2.

Z = (p1−p2)/√(p(1−p)(1/n1+1/n2)).

α/k.

R² = 1 − SSres/SStot.

Approx z critical for α (two-tailed).

Returns sum of y (placeholder).

df = n − 1.

y = a·e^(bx); returns predicted y.

P = C(a+b,a)C(c+d,c)/C(N,a+c).

F = s1²/s2².

z = (x̄−μ0)/(σ/√n).

Slope from 3 pairs.

MOE = z·σ/√n.

χ² = (|b−c|−1)²/(b+c).

z=(x−np)/√(np(1−p)).

p̂ = x/n.

Sum of y (placeholder).

Power = Φ(z − zα).

Two-tailed p from z.

Sum of y (placeholder).

x = μ + z·σ.

|x−x0|/|x0|.

e = y − ŷ.

SE = z·√(p(1−p)/n).

t = (x̄−μ)/(s/√n).

Two-sample t (equal var).

U = R1 − n1(n1+1)/2.

W = R1.

J = sens + spec − 1.

z = (x−μ)/σ.

z = (x̄−μ)/(σ/√n).

n = (z²·p(1−p))/E².

H = −Σ pi·log2(pi).

Accuracy = (TP+TN)/(TP+TN+FP+FN).

F = MS_between/MS_within (simplified).

P(A|B) = P(B|A)P(A)/P(B).

P=2/3 for second coin same as first.

Probability random chord > side of inscribed triangle (1/3, 1/2, 1/4).

P(shared) = 1 − 365!/((365−n)!·365^n).

P(both boys | at least one boy) = 1/3.

P(|X−μ|<kσ) ≥ 1 − 1/k².

Random coin flip (1=H,0=T).

P(k heads in n flips)=C(n,k)/2^n.

Approx expected longest streak ≈ log2(n).

C(n,k)=n!/(k!(n−k)!).

P(A|B) = P(A∩B)/P(B).

Returns accuracy.

Avg of d-sided die = (d+1)/2.

P = favorable/(sides^dice).

Random roll 1..sides.

E = Σ xi·pi (2 outcomes).

PPV = sens·prev/(sens·prev+(1−spec)(1−prev)).

Decimal odds: P=1/odds.

P(A∩B)=P(A)·P(B) (independent).

P = 1/C(n,k).

Switch wins 2/3.

Odds = p/(1−p).

Mixed game EV (illustrative).

chars^length.

P(n,k)=n!/(n−k)!.

p̂ = x/n.

Bayesian update of pre-test prob with LR.

P = favorable/total.

Independent: P=P1·P2·P3.

Avg sum = num·(sides+1)/2.

P = 1/C(n,k).

Random integer in [min,max].

RR = (a/(a+b))/(c/(c+d)).

Risk = events/total.

Payout = bet·multiplier.

Returns sensitivity.

Naive EV = 1.25·x.

Combinations = pool^length.

Random 1..10.

Sum of two d6.

Random 1..4.

P=1/6^dice for specific sum (any).

Random 1..6.

MOE = 1.645·σ/√n.

MOE = 1.96·σ/√n.

MOE = 2.576·σ/√n.

P(A∩B)=P(A)·P(B).

Min of 5.

C(n,k).

C(n+k−1,k).

Random 1..sides.

Random 1..100.

Random 1..20.

Decimal odds = 1/p.

Random in [min,max].

Random 1..20 (d20).

FPR = FP/(FP+TN).

Q1 of 5 sorted.

Frac odds = (1−p)/p.

Max of 5.

Min decimal.

Q1 − 1.5·IQR.

+: (1−p)/p·100; −: −p/(1−p)·100.

Min of 5.

Min decimal.

Min of 5.

P(A∪B)=P(A)+P(B)−P(A)P(B).

P(n,k).

n^k.

(part/total)·360.

part/total·100.

C(n,k).

favorable/total.

Sum of y (placeholder).

Random 1..6.

TP/(TP+FN).

TN/(TN+FP).

Q3 of 5 sorted.

P(sum=target) with 2d6.

Q3 + 1.5·IQR.