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Schooling · Class 10 · Mathematics · Statistics · Chapter on a page

CBSE Class 10 · Mathematics · NCERT Mathematics

Statistics: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

This note's current text has no applied fact-check on record.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

Mind map of Statistics: Key ideas, Formulas and facts, Worked examples, Watch out forKey ideasGrouped dataclass markmeanmedianmodeCumulative frequencyogiveFormulas and factsMean by Direct MethodMean by Assumed Mean MethodMean by Step Deviation MethodMedian of Grouped DataMode of Grouped DataEmpirical relationshipWorked examplesFinding mean using Step Deviation…Finding median of grouped dataFinding mode of grouped dataWatch out forUsing class limits instead of class…Confusing cumulative frequency with…Taking the wrong class as modal classForgetting to subtract cf…Using unequal class intervals…Statistics
The mind map as a list
  • Key ideas
    • Grouped data
    • class mark
    • mean
    • median
    • mode
    • Cumulative frequency
    • ogive
  • Formulas and facts
    • Mean by Direct Method
    • Mean by Assumed Mean Method
    • Mean by Step Deviation Method
    • Median of Grouped Data
    • Mode of Grouped Data
    • Empirical relationship
  • Worked examples
    • Finding mean using Step Deviation…
    • Finding median of grouped data
    • Finding mode of grouped data
  • Watch out for
    • Using class limits instead of class…
    • Confusing cumulative frequency with…
    • Taking the wrong class as modal class
    • Forgetting to subtract cf…
    • Using unequal class intervals…

What this chapter is about

Statistics is the branch of mathematics that deals with collecting, organising, analysing and interpreting numerical data. In Class 10, you move beyond simple averages to learn how to find the mean, median and mode for data that is grouped into class intervals. This is essential because real-world data — exam scores of hundreds of students, wages of workers, heights of people — is usually presented in grouped form.

Key ideas

  • Grouped data is data organised into class intervals (e.g., 10–20, 20–30) along with their frequencies; the exact values within each class are not known.
  • The class mark (or mid-value) of a class interval is calculated as (lower limit + upper limit) / 2 and represents all observations in that class.
  • The mean of grouped data can be found using three methods: Direct Method, Assumed Mean Method and Step Deviation Method — all give the same answer but differ in computational ease.
  • The median is the middle value of ordered data; for grouped data, we first find the median class (the class containing the n/2th observation) and then apply a formula.
  • The mode is the most frequently occurring value; for grouped data, the modal class is the class with the highest frequency.
  • Cumulative frequency is the running total of frequencies up to each class; it helps locate the median class and draw ogives.
  • An ogive (cumulative frequency curve) can be of two types: less than type and more than type; their intersection point gives the median.

Formulas and facts to remember

  • Mean by Direct Method:Mean = Σ(fᵢxᵢ) / Σfᵢwhere fᵢ is frequency and xᵢ is class mark.
  • Mean by Assumed Mean Method:Mean = a + (Σfᵢdᵢ / Σfᵢ)where a is assumed mean and dᵢ = xᵢ − a.
  • Mean by Step Deviation Method:Mean = a + h × (Σfᵢuᵢ / Σfᵢ)where h is class size and uᵢ = (xᵢ − a) / h.
  • Median of Grouped Data:Median = l + [(n/2 − cf) / f] × hwhere l = lower limit of median class, n = total frequency, cf = cumulative frequency before median class, f = frequency of median class, h = class size.
  • Mode of Grouped Data:Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × hwhere l = lower limit of modal class, f₁ = frequency of modal class, f₀ = frequency of class before modal class, f₂ = frequency of class after modal class.
  • Empirical relationship:3 × Median = Mode + 2 × Mean (approximate relationship).

Common mistakes

  • Using class limits instead of class marks in mean calculation → Always find class mark as (lower + upper)/2 before multiplying by frequency.
  • Confusing cumulative frequency with frequency when finding median → cf is the total before the median class, not the frequency of median class.
  • Taking the wrong class as modal class → Modal class is the class with highest frequency, not the highest class mark.
  • Forgetting to subtract cf (cumulative frequency before median class) in the median formula → The formula requires (n/2 − cf), not just n/2.
  • Using unequal class intervals without adjustment → Ensure all classes have equal width, or adjust frequencies accordingly.

Quick revision

  • Mean uses class marks; three methods (Direct, Assumed Mean, Step Deviation) all give the same answer.
  • Median class contains the (n/2)th observation; use cumulative frequency to locate it.
  • Mode formula needs the modal class (highest frequency) and frequencies of its neighbours.
  • Ogives are cumulative frequency curves; the x-coordinate where less-than and more-than ogives meet gives the median.
  • Always check: Σfᵢ = n (total observations) before applying any formula.