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NCERT Class 11 Mathematics Chapter 13

Statistics for Class 11 Maths and JEE: mean, median and mode, range, mean deviation, variance and standard deviation of grouped and ungrouped data.

6 topics Updated 8 Nov 2026

For: Class 11 and JEE, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 13 “Statistics”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.9 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Mean, median and mode

    Formulas for lists and frequency tables, the grouped median, mean vs median and why an average is not enough.

    NCERT Section 13.1 12 min read 6 solved examples 13 practice questions

  2. Mode of ungrouped and grouped data

    The mode formula for grouped data (JEE Main): the modal class, what l, h, f, f and f mean, why it works and bimodal data, with solved examples.

    JEE only 12 min read 6 solved examples 12 practice questions

  3. Measures of dispersion

    Range, quartile deviation, mean deviation and SD compared, why deviations cancel, with solved examples.

    NCERT Section 13.2 10 min read 6 solved examples 12 practice questions

  4. Range

    The formula for lists, frequency tables and grouped data, coefficient of range, its limits and solved examples.

    NCERT Section 13.3 8 min read 6 solved examples 12 practice questions

  5. Mean deviation

    Formulas about the mean and the median for lists, frequency tables and grouped data, with every NCERT example worked.

    NCERT Section 13.4 19 min read 7 solved examples 12 practice questions

  6. Variance and standard deviation

    Formulas for lists, frequency tables and grouped data, the short-cut method and solved examples.

    NCERT Section 13.5 19 min read 7 solved examples 12 practice questions

Key formulas in this chapter

Mean, median and mode

  • x̄ = Σfx/N, N = Σf
  • Σ(x − x̄) = 0
  • median: ((n + 1)/2)th value (n odd); mean of the (n/2)th and (n/2 + 1)th (n even)
  • M = l + ((N/2 − C)/f) × h

Mode

  • Mode = l + ((f − f)/(2f − f − f)) × h
  • f = 0 if the modal class is first; f = 0 if it is last
  • mode ≈ 3 median − 2 mean (moderately lopsided data)

Measures of dispersion

  • range = maximum − minimum
  • QD = (Q − Q)/2
  • Σ(x − x̄) = 0
  • adding a constant c: range, QD, MD, variance and SD unchanged
  • multiplying by k: range, QD, MD, SD × |k|; variance × k

Range

  • range = maximum − minimum
  • grouped class span: upper boundary of last occupied class − lower boundary of first occupied class
  • coefficient of range = (max − min)/(max + min), max + min > 0 (beyond NCERT)
  • adding a constant c: range unchanged; multiplying by k: range × |k|

Mean deviation

  • M.D.(a) = (1/n) Σ|x − a|
  • M.D.(a) = (1/N) Σf|x − a|, N = Σf
  • x̄ = (1/N) Σfx
  • x̄ = A + h × (Σfd)/N, d = (x − A)/h
  • M = l + ((N/2 − C)/f) × h
  • M.D.(M) ≤ M.D.(x̄), M the median of the same data
  • x → kx + c: M.D. × |k|

Variance and SD

  • σ = (1/n) Σ(x − x̄)
  • σ = (1/N) Σf(x − x̄)
  • σ = (1/N) Σfx − x̄
  • σ = (1/N) √[NΣfx − (Σfx)]
  • yi = (xi − A)/h, h > 0: x̄ = A + hȳ, σx = hσy
  • y = kx + c: σy^2 = k2σx^2, σy = |k|σx
  • Σx = nx̄, Σx = n(σ + x̄)

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