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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Chapter Exercises & Topics

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Exercise 10.1 45 mins

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Exercise 10.2 45 mins

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Exercise 10.3 45 mins

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

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Exercise 10.4 45 mins

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

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

$$\text{Range} = L - S, \quad \text{Coeff of Range} = \frac{L - S}{L + S}$$
$$\text{IQR} = Q_3 - Q_1, \quad \text{Quartile Deviation (QD)} = \frac{Q_3 - Q_1}{2}$$
$$MD(\bar{x}) = \frac{\sum f_i |x_i - \bar{x}|}{N}, \quad MD(M) = \frac{\sum f_i |x_i - M|}{N}$$
$$\text{Coeff of } MD(\bar{x}) = \frac{MD(\bar{x})}{\bar{x}}$$
$$\sigma^2 = \frac{\sum f_i(x_i - \bar{x})^2}{N} = \frac{\sum f_i x_i^2}{N} - \bar{x}^2$$
$$\sigma = \sqrt{\sigma^2}, \quad CV = \frac{\sigma}{\bar{x}} \times 100$$
$$Q_k = \text{Value of } \left(\frac{k(N+1)}{4}\right)^{\text{th}} \text{ term}$$
$$P_k = \text{Value of } \left(\frac{k(N+1)}{100}\right)^{\text{th}} \text{ term}$$
$$\text{Percentile Rank} = \frac{B + 0.5E}{N} \times 100$$