Summaries
| Quantity |
Formula |
Grade |
| mean |
x̄ = Σx ÷ n |
8 |
| median |
middle of sorted values; position (n + 1) ÷ 2 |
8 |
| range |
max − min |
8 |
| quartiles, IQR |
Q1, Q3 (medians of lower/upper halves); IQR = Q3 − Q1 |
9–10 |
| outlier fences |
Q1 − 1.5 × IQR, Q3 + 1.5 × IQR |
9–10 |
| variance, SD (sample) |
s² = Σ(x − x̄)² ÷ (n − 1); s = √s² |
10 |
| z-score |
z = (x − x̄) ÷ s |
10 |
| coefficient of variation |
s ÷ x̄ |
10 |
| 68–95 rule |
bell-shaped data: ≈ 68% within 1 SD, ≈ 95% within 2 SD |
10 |
Rates and change
| Quantity |
Formula |
Grade |
| rate |
numerator ÷ denominator × 100 / 1,000 / 100,000 |
8–9 |
| ratio |
e.g. sex ratio = males ÷ females × 100 |
9 |
| weighted group rate |
Σ numerators ÷ Σ denominators |
9 |
| percentage points |
new % − old % |
8 |
| percent change |
(new − old) ÷ old × 100 |
8 |
| annual growth rate |
(new ÷ old)^(1/years) − 1 |
9 |
| index number |
value ÷ base value × 100 |
9 |
| angle in a pie chart |
share × 360° |
8 |
Relationships and models
| Quantity |
Formula |
Grade |
| correlation |
r = Σ(z_x × z_y) ÷ (n − 1), −1 ≤ r ≤ 1 |
9–10 |
| least-squares line |
ŷ = a + b x; b = r × s_y ÷ s_x; a = ȳ − b x̄ |
10 |
| residual |
y − ŷ |
10 |
| R² |
1 − Σ(residual²) ÷ Σ(y − ȳ)²; for one predictor R² = r² |
10–11 |
| logistic function |
p = 1 ÷ (1 + e^(−z)), z = b₀ + b₁x₁ + … |
12 |
| odds, odds ratio |
odds = p ÷ (1 − p); OR per unit = e^b |
12 |
| MAE, RMSE |
mean |
y − ŷ |
Uncertainty and testing
| Quantity |
Formula / rule |
Grade |
| standard error of a mean |
≈ s ÷ √n (quadruple n → halve SE) |
11 |
| rough 95% interval |
estimate ± 2 × SE |
11 |
| bootstrap 95% CI |
2.5th to 97.5th percentiles of bootstrap statistics |
11 |
| permutation p-value |
share of shuffled statistics at least as extreme as observed (two-sided: compare absolute values) |
11 |
| SE of a proportion |
≈ √(p(1 − p) ÷ n) |
12 |
Classification metrics
| Metric |
Formula |
| accuracy |
(TP + TN) ÷ all |
| precision |
TP ÷ (TP + FP) |
| recall (sensitivity) |
TP ÷ (TP + FN) |
| specificity |
TN ÷ (TN + FP) |
| F1 |
2 × precision × recall ÷ (precision + recall) |
| selection rate |
flagged ÷ group size |
Time and place
| Quantity |
Formula |
Grade |
| BS → AD year |
− 57 (mid-April to December), − 56 (January to mid-April) |
9 |
| additive seasonal index |
month mean − overall mean (sum = 0) |
11 |
| multiplicative seasonal index |
month mean ÷ overall mean (average = 1) |
11 |
| anomaly |
observed − baseline for that month |
10 |
| trend per decade |
slope (per year) × 10 |
10 |
| km per degree |
latitude ≈ 111 km; longitude ≈ 111 × cos(latitude) km |
11 |
| haversine distance |
d = 2R·arcsin √(sin²(Δφ/2) + cos φ₁ cos φ₂ sin²(Δλ/2)), R = 6,371 km |
11 |
Unit conversions often met in Nepali data
1 lakh = 100,000 · 1 crore = 10,000,000 · 1 ropani = 508.72 m² · 1 bigha = 6,772.63 m² · rain mm/day × days = mm per
month · 1 µg/m³ = one-millionth of a gram per cubic metre.