Exercise 11.2 Class 10 Math Solutions – Measures of Dispersion, Punjab Board

Solved Exercise 11.2 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering measures of dispersion: Range, Variance (S²), and Standard Deviation (S) for ungrouped and grouped frequency distributions.

This page provides complete solved solutions for Exercise 11.2 from Unit 11: Information Handling, Class 10 Mathematics, Punjab Board (PCTB). It covers statistical measures of dispersion including Range (R = X_max - X_min), Variance (direct and short-cut formulas), and Standard Deviation (S = √Variance) for both ungrouped datasets and grouped frequency distributions. All calculation tables and numerical steps are prepared for Matric Part 2 students.
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Exercise Overview

Exercise 11.2 in Unit 11: Information Handling of Class 10 Punjab Board Mathematics focuses on statistical measures of dispersion. Moving beyond central tendencies (mean, median, mode), this exercise equips students with analytical tools to measure the spread, scatter, and consistency of numerical data distributions.

The exercise systematically covers the definition, formulas, and computational methods for Range, Variance (S²), and Standard Deviation (S). Students learn both definitional and computational shortcut formulas across ungrouped observations and grouped frequency tables (using class boundaries, mid-values X, and frequencies f). Calculating Standard Deviation as the positive square root of variance provides a direct, unit-consistent metric for comparing dataset variability.

In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), measures of dispersion from Exercise 11.2 are standard high-scoring 4-mark short questions and Section C structured calculation problems. Practicing these verified, step-by-step solutions with organized frequency tables ensures arithmetic precision and secures full marks in board exams.

FAQs

Are these Exercise 11.2 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 11 Exercise 11.2 measures of dispersion for the 2026-2027 session.
What is meant by measures of dispersion in Statistics?
Measures of dispersion quantify the extent of spread, variability, or scatter of individual data observations around a central value (such as the arithmetic mean).
How is the Range calculated for a given dataset?
Range is the simplest measure of dispersion, calculated as the difference between the maximum value (X_max) and minimum value (X_min) in the dataset: Range = X_max - X_min.
What is Variance and what is its standard mathematical formula?
Variance (S²) is the mean of squared deviations from the arithmetic mean. For ungrouped data, S² = Σ(X - X̄)² / n = (ΣX² / n) - (ΣX / n)².
What is Standard Deviation and how does it relate to Variance?
Standard Deviation (S or σ) is the positive square root of the variance: S = √Variance. It measures dispersion in the original units of measurement.
How are Variance and Standard Deviation calculated for grouped frequency data?
For grouped frequency distributions: S² = (ΣfX² / Σf) - (ΣfX / Σf)², and Standard Deviation S = √[(ΣfX² / Σf) - (ΣfX / Σf)²], where X represents class midpoints and f is class frequency.
Are complete step-by-step calculation tables provided for Exercise 11.2 numericals?
Yes, every problem includes organized statistical tables with X, f, fX, X², and fX² columns alongside clear algebraic substitutions.
Can students read these Exercise 11.2 solutions online?
Yes, the complete solved PDF notes for Exercise 11.2 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 11.2 solutions free for students?
Yes, all Exercise 11.2 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.