Statistics Module 5: Central Tendency & Dispersion

Module 5: Measures of Central Tendency and Dispersion

• Arithmetic Mean (Ungrouped Data): X̄ = ΣX / N
• Arithmetic Mean (Grouped Data): X̄ = Σfx / Σf
• Median (Ungrouped Data): The middle value in arranged data. (n + 1) / 2
• Median (Grouped Data): Median = L₁+ (n/2 - CF) * i / f
  • L₁ = Lower limit of the median class
  • n = total frequency
  • CF = Cumulative frequency of the class preceding the median class
  • i = class interval
  • f = frequency of the median class
• Mode: The most frequently occurring value.
  • Mode = L+ [(Δ₁ / (Δ₁ + Δ₂)] * i
  • L = lower limit of modal class
  • Δ₁ = difference between the frequency of modal class and the frequency of the class preceding it
  • Δ₂ = difference between the frequency of modal class and the frequency of the class succeeding it
  • i = class interval

Module 5: Measures of Dispersion

• Range: H - L (where H= highest value and L=lowest value)

• Coefficient of Range: (H-L) / (H+L)

• Standard Deviation (Ungrouped Data): √Σ(X - X̄)² / N

• Standard Deviation (Grouped Data): √Σf(X - X̄)² / Σf

• Mean Deviation (Ungrouped Data): Σ|X - X̄| / N

• Mean Deviation (Grouped Data): Σf|X - X̄| / Σf

• Quartile Deviation: (Q₃ - Q₁ ) / 2

  • Q₁ = First quartile, Q₃ = Third quartile

• Quartiles (Continuous Data): Q1 = L₁ + [(n/4) - CF] * i / f Q3 = L₁ + [(3n/4) - CF] * i / f

  • L₁ - Lower limit of the quartile class
  • n – Total frequency
  • cf - cumulative frequency of the class before the quartile class
  • i - Class interval
  • f - Frequency of the quartile class

Module 4: Index Numbers & Time Series

• Simple Index: SI = (Pₙ/P₀) * 100

  • Pₙ = Price in current period
  • P₀ = Price in base period

• Compound Index: C.I = A - P / [(1+ (R/100)) ^ n-1 ]

  • A= Final Amount
  • P= Principle
  • R= Rate
  • n= Number of periods

• EMI Calculation: EMI = PxRx(1+R)^N/ [(1+R)^N-1)]

  • P = Principle
  • R = Rate
  • N = Number of periods

Module 3: Progressions

• Arithmetic Progression (nth term): aₙ = a₁ + (n - 1)d
• Arithmetic Progression (Sum): Sₙ = n/2 [2a₁ + (n - 1)d] or Sn = n/2 (a + l)
• Geometric Progression (nth term): aₙ = a₁ * rⁿ⁻¹
• Geometric Progression(Sum): Sₙ = a₁ (1 - rⁿ) / (1 - r)

This quiz covers key concepts from Module 5 of statistics, focusing on measures of central tendency such as the mean, median, and mode, along with measures of dispersion like range. Test your understanding of ungrouped and grouped data calculations. Perfect for students looking to strengthen their statistical knowledge.