PYQs
Practise questions grouped by chapter and source year.
Practice questions are organised using the years and labels in our source collection. Work through the solutions with your teacher; these are not a complete official examination paper.
Practice question 1
Source year: 20253 marksFind mean of frequency distribution. [CBSE 2025]
Practice question 2
Source year: 20243 marksFind mode and median. [CBSE 2024]
Practice question 3
Source year: 20253 marksFind mean of following frequency distribution: 0-20(6), 20-40(8), 40-60(10), 60-80(12), 80-100(6). [CBSE 2025]
Practice question 4
Source year: 20243 marksFind mode and median from data: 5,3,6,5,4,5,2,8,6,5,4,8,3,4,5,4,8,2,5,4. [CBSE 2024]
Practice question 5
Source year: 20233 marksDraw ogive for given data and find median. [CBSE 2023]
Practice question 6
Source year: 20223 marksFind mean using assumed mean method. [CBSE 2022]
Formulae
Revisit important relationships and quick revision formulae.
Mean
Mean = Σfx / Σf
Median
Median = l + [(n/2 - cf)/f] × h
Mean (Ungrouped)
Mean = Sum of observations / Number of observations\nMean = Σx / n
Mean (Grouped)
Direct Method: Mean = Σfx / Σf\nAssumed Mean: Mean = a + Σfd / Σf\nStep Deviation: Mean = a + (Σfu / Σf) × h
Median (Grouped)
Median = l + [(n/2 - cf) / f] × h\nl = lower limit of median class\nn = total frequency\ncf = cumulative frequency before median class\nf = frequency of median class\nh = class width
Mode (Grouped)
Mode = l + [(f₁-f₀) / (2f₁-f₀-f₂)] × h\nl = lower limit of modal class\nf₁ = frequency of modal class\nf₀ = frequency before modal class\nf₂ = frequency after modal class\nh = class width
Derivations
Work through the reasoning behind key concepts.
Relation: 3Median = Mode + 2Mean
This is an empirical relation that holds approximately for moderately skewed distributions. It's useful for finding one measure when other two are known. Exact for perfectly symmetrical distributions.
Relation between Mean, Median, Mode
3 Median = Mode + 2 Mean (empirical relation)
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