23/05/2025, 22:33 Business Statistics Notes - BCOM 106
BUSINESS STATISTICS
Course Code: BCOM 106 | Credits: 4 | L-4, T-0
University: Guru Gobind Singh Indraprastha University, Delhi
Program: Bachelor of Commerce (Honours)
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,23/05/2025, 22:33 Business Statistics Notes - BCOM 106
UNIT 1: STATISTICAL DATA AND DESCRIPTIVE STATISTICS
1.1 Nature and Classification of Data
Data: Raw facts and figures collected for analysis and interpretation to derive meaningful insights for
decision-making.
Shifting of Origin:
Purpose: To simplify calculations by changing the origin (zero point) of time variable.
If original equation is Y = a + bt
After shifting origin by k units: Y = a' + bt'
where t' = t - k and a' = a + bk
Conversion of Linear Equations:
Annual to Quarterly:
If annual trend is Y = a + bt (where t is in years)
Quarterly trend: Y = a + b(t/4) where t is in quarters
Annual to Monthly:
If annual trend is Y = a + bt (where t is in years)
Monthly trend: Y = a + b(t/12) where t is in months
Quarterly to Annual:
If quarterly trend is Y = a + bt (where t is in quarters)
Annual trend: Y = a + 4bt where t is in years
Monthly to Annual:
If monthly trend is Y = a + bt (where t is in months)
Annual trend: Y = a + 12bt where t is in years
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, 23/05/2025, 22:33 Business Statistics Notes - BCOM 106
IMPORTANT FORMULAS SUMMARY
Descriptive Statistics
Measure Formula
Arithmetic Mean x̄ = Σx/n
Geometric Mean G.M. = ⁿ√(x₁ × x₂ × ... × xₙ)
Harmonic Mean H.M. = n/Σ(1/x)
Standard Deviation σ = √[Σ(x - x̄ )²/n]
Coefficient of Variation C.V. = (σ/x̄ ) × 100
Skewness (Pearson) Skₑ = 3(Mean - Median)/σ
Probability Distributions
Distribution Probability Function Mean Variance
Binomial P(X = r) = ⁿCᵣpʳqⁿ⁻ʳ np npq
Poisson P(X = r) = e⁻λλʳ/r! λ λ
Normal Z = (X - μ)/σ μ σ²
Correlation and Regression
Measure Formula
Correlation Coefficient r = Σ(x-x̄ )(y-ȳ)/√[Σ(x-x̄ )²Σ(y-ȳ)²]
Regression Y on X Y - ȳ = byx(X - x̄ )
Regression X on Y X - x̄ = bxy(Y - ȳ)
Regression Coefficients byx = r(σy/σx), bxy = r(σx/σy)
Index Numbers
file:///C:/Users/aksha/OneDrive/Documents/business_stats_notes.html 3/21
BUSINESS STATISTICS
Course Code: BCOM 106 | Credits: 4 | L-4, T-0
University: Guru Gobind Singh Indraprastha University, Delhi
Program: Bachelor of Commerce (Honours)
file:///C:/Users/aksha/OneDrive/Documents/business_stats_notes.html 1/21
,23/05/2025, 22:33 Business Statistics Notes - BCOM 106
UNIT 1: STATISTICAL DATA AND DESCRIPTIVE STATISTICS
1.1 Nature and Classification of Data
Data: Raw facts and figures collected for analysis and interpretation to derive meaningful insights for
decision-making.
Shifting of Origin:
Purpose: To simplify calculations by changing the origin (zero point) of time variable.
If original equation is Y = a + bt
After shifting origin by k units: Y = a' + bt'
where t' = t - k and a' = a + bk
Conversion of Linear Equations:
Annual to Quarterly:
If annual trend is Y = a + bt (where t is in years)
Quarterly trend: Y = a + b(t/4) where t is in quarters
Annual to Monthly:
If annual trend is Y = a + bt (where t is in years)
Monthly trend: Y = a + b(t/12) where t is in months
Quarterly to Annual:
If quarterly trend is Y = a + bt (where t is in quarters)
Annual trend: Y = a + 4bt where t is in years
Monthly to Annual:
If monthly trend is Y = a + bt (where t is in months)
Annual trend: Y = a + 12bt where t is in years
file:///C:/Users/aksha/OneDrive/Documents/business_stats_notes.html 2/21
, 23/05/2025, 22:33 Business Statistics Notes - BCOM 106
IMPORTANT FORMULAS SUMMARY
Descriptive Statistics
Measure Formula
Arithmetic Mean x̄ = Σx/n
Geometric Mean G.M. = ⁿ√(x₁ × x₂ × ... × xₙ)
Harmonic Mean H.M. = n/Σ(1/x)
Standard Deviation σ = √[Σ(x - x̄ )²/n]
Coefficient of Variation C.V. = (σ/x̄ ) × 100
Skewness (Pearson) Skₑ = 3(Mean - Median)/σ
Probability Distributions
Distribution Probability Function Mean Variance
Binomial P(X = r) = ⁿCᵣpʳqⁿ⁻ʳ np npq
Poisson P(X = r) = e⁻λλʳ/r! λ λ
Normal Z = (X - μ)/σ μ σ²
Correlation and Regression
Measure Formula
Correlation Coefficient r = Σ(x-x̄ )(y-ȳ)/√[Σ(x-x̄ )²Σ(y-ȳ)²]
Regression Y on X Y - ȳ = byx(X - x̄ )
Regression X on Y X - x̄ = bxy(Y - ȳ)
Regression Coefficients byx = r(σy/σx), bxy = r(σx/σy)
Index Numbers
file:///C:/Users/aksha/OneDrive/Documents/business_stats_notes.html 3/21
