Home Class 11 Applied Maths Chapter 10: Measures of Dispersion and Percentiles
CBSE Applied Maths (2026-27) Unit V: Descriptive Statistics Weightage: ~10 Marks in Unit

Chapter 10: Measures of Dispersion and Percentiles

Compute range, quartile deviation, mean deviation, variance, standard deviation, coefficient of variation, and percentile ranks.

4 Exercises
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Interactive Quizzes & Solutions

Chapter Exercises & Topics

Select any exercise to access theory notes, formulas, practice drills, and mini tests.

Exercise 10.1 45 mins

Measures of Dispersion

  • Meaning and purpose of dispersion in statistical analysis
  • Range and Coefficient of Range
  • Quartile Deviation (Semi-interquartile range) and Interquartile Range (IQR)
Study Exercise Mini Test
Exercise 10.2 45 mins

Mean Deviation

  • Mean deviation about Mean (ungrouped and grouped frequency distributions)
  • Mean deviation about Median
  • Coefficients of Mean Deviation
Study Exercise Mini Test
Exercise 10.3 45 mins

Standard Deviation and Variance

  • Calculation of Variance (σ^2) and Standard Deviation (σ) for raw, discrete, and continuous series
  • Shortcut and step-deviation methods
  • Properties of standard deviation (effect of change of origin and scale)
  • Coefficient of Variation (CV = (σ/x̄) × 100) for stability/consistency comparison
Study Exercise Mini Test
Exercise 10.4 45 mins

Percentiles and Quartiles

  • Calculation of Quartiles (Q1, Q2, Q3), Deciles, and Percentiles
  • Percentile Rank formula and interpretation in comparative scoring and standardized testing
Study Exercise Mini Test

Chapter 10 Core Formula Sheet

Quick-glance formula revision for examination and numerical problem-solving:

  • $$Range = L - S, \quad Coeff of Range = L - SL + S$$
  • $$IQR = Q_3 - Q_1, \quad Quartile Deviation (QD) = Q_3 - Q_12$$
  • $$MD(\bar{x}) = ∑ f_i |x_i - \bar{x}|N, \quad MD(M) = ∑ f_i |x_i - M|N$$
  • $$Coeff of MD(\bar{x}) = MD(\bar{x})\bar{x}$$
  • $$σ^2 = ∑ f_i(x_i - \bar{x})^2N = ∑ f_i x_i^2N - \bar{x}^2$$
  • $$σ = √σ^2, \quad CV = σ\bar{x} × 100$$
  • $$Q_k = Value of (k(N+1)4)th term$$
  • $$P_k = Value of (k(N+1)100)th term$$
  • $$Percentile Rank = B + 0.5EN × 100$$
Ch 9: Probability All Chapters Syllabus Ch 11: Correlation Analysis