Ch 13 moves beyond central tendency to dispersion — how spread out data is. Students learn range, mean deviation, variance, and standard deviation for both grouped and ungrouped data.
Range = highest − lowest value (simplest measure). Mean deviation = Σ|xᵢ − x̄|/n for ungrouped data, Σfᵢ|xᵢ − x̄|/Σfᵢ for grouped data. It measures the average absolute deviation from mean or median.
Variance σ² = Σ(xᵢ − x̄)²/n. Standard deviation σ = √(variance). Shortcut: σ² = (Σxᵢ²/n) − (x̄)². For grouped data: σ² = (Σfᵢxᵢ²/N) − (Σfᵢxᵢ/N)² where N = Σfᵢ.
CV = (σ/x̄) × 100. Used to compare variability of two data sets with different units or means. Higher CV = more variability.
Download: https://ncert.nic.in/textbook/pdf/kemh113.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
Standard deviation has better mathematical properties — it's differentiable and works with the normal distribution. Mean deviation uses absolute values which are harder to manipulate algebraically. SD is the universally preferred measure of dispersion.
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