Ch 13 covers mean, median, and mode of grouped (frequency distribution) data, and introduces cumulative frequency graphs (ogives) as visual tools for finding the median.
Direct method: x̄ = Σfᵢxᵢ/Σfᵢ. Assumed mean method: x̄ = a + Σfᵢdᵢ/Σfᵢ (dᵢ = xᵢ − a). Step-deviation method: x̄ = a + (Σfᵢuᵢ/Σfᵢ) × h (uᵢ = dᵢ/h). Choose the method based on data size.
Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h, where l = lower limit of modal class, f₁ = its frequency, f₀ and f₂ = adjacent classes. Median = l + [(n/2−cf)/f] × h, where cf = cumulative frequency of class preceding median class.
Less-than ogive: plot upper class limits vs cumulative frequency. More-than ogive: plot lower limits vs cumulative frequency. The x-coordinate of the intersection of both ogives gives the median.
Download: https://ncert.nic.in/textbook/pdf/jemh113.pdf | Complete book: https://ncert.nic.in/textbook/pdf/jemh1ps.zip
Mean uses all data values and is best for symmetric data. Median is best for skewed data or data with outliers. Mode identifies the most common value. For CBSE Board exams, you need all three methods.
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