📐 3.5 क्षेत्रफल तथा घनफल (Mensuration)

Rectangle (आयत): Area = l×b | Perimeter = 2(l+b)
Square (वर्ग): Area = a² | Perimeter = 4a
Triangle (त्रिभुज): Area = ½×b×h | Heron’s: √[s(s-a)(s-b)(s-c)], s=(a+b+c)/2
Circle (वृत्त): Area = πr² | Circumference = 2πr (π≈3.14159)
Cylinder (बेलनाकार): Volume = πr²h | Lateral SA = 2πrh
Cube: Volume = a³ | Surface Area = 6a²
Cuboid: Volume = l×b×h
Banking Example: बैंकको Vault Room को आयाम: 5m × 4m × 3m
Volume = 5 × 4 × 3 = 60 m³
Floor Area = 5 × 4 = 20 m²

📊 3.6–3.7 तथ्याङ्क र मध्यक (Statistics and Averages)

Mean (अंकगणितीय मध्य):
Simple Mean = ΣX / n (ungrouped)
Weighted Mean = ΣwX / Σw
Grouped Mean = ΣfX / Σf (f=frequency, X=mid-value)

Median (मध्यिका):
Odd n: Middle value of sorted data
Even n: Average of n/2 and (n/2+1) values

Mode (बहुलक): Most frequently occurring value

Range (परास): Max – Min
Standard Deviation (मानक विचलन): σ = √[Σ(X-X̄)²/n]

Weighted Average Lending Rate Example:
Bank A lends: Rs.10 Cr @ 12%, Rs.20 Cr @ 11%, Rs.30 Cr @ 10%
WALR = (10×12 + 20×11 + 30×10) / (10+20+30)
= (120 + 220 + 300) / 60 = 640/60 = १०.६७%

Median Example: Data: 5, 3, 8, 2, 9, 1, 7 → Sorted: 1,2,3,5,7,8,9 → Median = 5

Measure NRB/Banking Application
Arithmetic Mean Weighted Average Lending/Deposit Rate (WALR/WADR)
Weighted Mean Portfolio Average Return, WACC
Median Median Income for Loan Eligibility
Standard Deviation Risk Measurement — Volatility of Returns
Mode Most common Loan Amount, Cheque Amount analysis

📈 3.8 मूल्य सूचकांक (Price Index)

परिभाषा: मूल्य सूचकांक भनेको एक निश्चित आधार वर्षको मूल्यको तुलनामा हालको मूल्यको अनुपात देखाउने सांख्यिकीय उपकरण हो।

Simple Price Index:
Price Index = (Current Price / Base Price) × 100

Laspeyres Index (Base Period Quantity):
L = [Σ(P₁×Q₀) / Σ(P₀×Q₀)] × 100

Paasche Index (Current Period Quantity):
P = [Σ(P₁×Q₁) / Σ(P₀×Q₁)] × 100

Fisher’s Ideal Index = √(L × P)

Inflation Rate = [(CPI Current – CPI Previous) / CPI Previous] × 100

सूचकांक पूर्ण नाम NRB/नेपालमा प्रयोग
CPI Consumer Price Index नेपाल CBS ले मासिक calculate; NRB Inflation Target Base
WPI Wholesale Price Index Wholesale market prices; CBS Nepal
NEPSE Index Nepal Stock Exchange Index Share Market health indicator; SEBON/NRB
GDP Deflator Nominal GDP / Real GDP × 100 Broad inflation measure; NPC/MoF
CPI Calculation:
Base Year (2076/77) CPI = 100 | Current Year CPI = 115
Inflation = [(115 – 100) / 100] × 100 = १५%

NRB Context: NRB ले मौद्रिक नीति (Monetary Policy) मार्फत Inflation ७% भित्र राख्ने लक्ष्य राख्छ। CPI बढ्दा NRB Policy Rate बढाउँछ।

✍️ ५ अंक — “मूल्य सूचकांकको महत्त्व र प्रकारहरू”

  1. परिभाषा: आधार वर्षसँग तुलना गरी मूल्य परिवर्तन मापन गर्ने उपकरण
  2. CPI: उपभोक्ता वस्तु/सेवाको मूल्य — Inflation मापनको मुख्य आधार
  3. WPI: थोक बजारको मूल्य — Production cost indicator
  4. NRB उपयोग: Inflation target (≤7%) निर्धारण; Monetary Policy calibration
  5. Real vs Nominal: Real Value = Nominal Value / (Price Index/100)
🔑 Statistics Formulas:
Mean = ΣfX/Σf | Median = L + [(n/2-cf)/f]×h (grouped)
CPI Inflation = (CPI_t – CPI_t-1)/CPI_t-1 × 100
NRB Inflation Target: ≤ 7% (मौद्रिक नीति लक्ष्य)
Nepal CPI Base Year: 2076/77 (current)
💡 सम्भावित प्रश्न: “CPI र Inflation को सम्बन्ध” | “Weighted Average Rate गणना” | “Laspeyres र Paasche Index को फरक” | “Standard Deviation को महत्त्व”