Statistics – NCERT Class 11 Mathematics Chapter 13 – Measures of Central Tendency, Dispersion, Variance, and Standard Deviation

Introduces the science of statistics focusing on the collection, analysis, and interpretation of data. Discusses measures of central tendency including mean, median, and mode; various measures of dispersion such as range, mean deviation, variance, and standard deviation; methods for ungrouped and grouped data; illustrative examples and exercises; and historical evolution of statistics with key contributors.

Updated: 8 months ago

Categories: NCERT, Class XI, Mathematics, Statistics, Central Tendency, Dispersion, Variance, Standard Deviation, Chapter 13

Tags: Statistics, Measures of Central Tendency, Mean, Median, Mode, Measures of Dispersion, Range, Mean Deviation, Variance, Standard Deviation, Data Analysis, Frequency Distribution, Grouped Data, Ungrouped Data, History of Statistics, NCERT Class 11, Mathematics, Chapter 13

Statistics: Class 11 NCERT Chapter 13 - Ultimate Study Guide, Notes, Questions, Quiz 2025

Full Chapter Summary & Detailed Notes - Statistics Class 11 NCERT

Overview & Key Concepts

Chapter Goal: Measures of dispersion beyond central tendency. Focus: Range, mean deviation (ungrouped/grouped). Exam Focus: Calculations, tables, steps. 2025 Updates: Batsmen examples emphasized. Fun Fact: Karl Pearson (1857-1936) advanced stats. Core Idea: Scatter around center. Real-World: Cricket scores variability. Ties: Ch5 (mean/median). Expanded: Ungrouped to grouped, discrete/continuous from PDF.
Wider Scope: Variability via range/deviations (PDF covers intro, range, mean dev up to continuous).
Expanded Content: Examples, tables, steps.

13.1 Introduction

Statistics analyzes data; central tendency (mean/median/mode) insufficient alone. Need dispersion for scatter. Batsmen A (0-117, mean 53) vs B (46-60, mean 53): A scattered, B clustered (Figs 13.1-2). Dispersion: Single number for variability.

13.2 Measures of Dispersion

Range, quartile dev, mean dev, std dev (study all except quartile). Depend on central tendency.

13.3 Range

Max - Min. A:117, B:14. Rough scatter idea, ignores center.

13.4 Mean Deviation

Mean of absolute deviations from 'a' (mean/median). Sum |x_i - a| / n =0 if signed (from mean). MD(a) = $$\sum |x_i - a| / n$$. Common: From mean/median.

13.4.1 Ungrouped Data

Steps: Compute a, deviations, absolutes, mean. Ex1: Data 6,7,10,12,13,4,8,12; mean=9, MD=2.75. Ex2: 20 obs, mean=10, MD=6.2. Ex3: Median=9, MD=5.27.

13.4.2 Grouped Data

(a) Discrete: $$\bar{x} = \sum f_i x_i / N$$, MD= $$\sum f_i |x_i - \bar{x}| / N$$. Median: cf >= N/2. Ex4: MD mean=2.3. Ex5: MD median=4.97.

(b) Continuous: Midpoints as x_i. Ex: Marks 0-10 etc., proceed as discrete.

Summary

Dispersion complements center; range quick, mean dev detailed. Master: Steps/tables, absolute values. Apps: Performance analysis. Mantra: Scatter needs absolutes.

Why This Guide Stands Out

Tables from PDF, batsmen intuition, step-by-step devs, free 2025 with MathJax.

Key Themes & Tips

Aspects: Rough (range) to deviation-based.
Tip: Always absolute; arrange for median.

Exam Case Studies

Batsmen variability; grouped calcs.

Project & Group Ideas

Plot scores in Excel, compute devs.
Apps: Cricket stats analyzer.

Key Definitions & Terms - Complete Glossary

All terms from chapter; detailed with examples, relevance. Expanded: 15+ terms with depth.

Dispersion

Scatter of data. Relevance: Variability. Ex: Batsmen ranges. Depth: Around center.

Range

Max - Min. Relevance: Quick spread. Ex: A=117, B=14. Depth: Ignores center.

Mean Deviation

Mean |x_i - a|. Relevance: Absolute scatter. Ex: From mean=2.75 Ex1. Depth: a=mean/median.

Central Tendency

Mean/median/mode. Relevance: Center. Ex: Both 53. Depth: Insufficient alone.

Absolute Deviation

|x - a|. Relevance: Distance. Ex: Drop signs. Depth: Sum / n.

Ungrouped Data

Individual obs. Relevance: Simple calc. Ex: Ex1 list. Depth: Direct sum.

Grouped Data

Frequency dist. Relevance: Large data. Ex: Discrete table. Depth: f_i weights.

Discrete Frequency

Distinct x_i, f_i. Relevance: Exact values. Ex: Ex4 x=2 f=2. Depth: cf for median.

Continuous Frequency

Class intervals. Relevance: Ranges. Ex: Marks 0-10. Depth: Midpoints.

Cumulative Frequency

Running total f. Relevance: Median find. Ex: Table 13.2 cf=18. Depth: >=N/2.

MD about Mean

From $$\bar{x}$$. Relevance: Common. Ex: 2.3 Ex4. Depth: Weighted sum.

MD about Median

From M. Relevance: Robust. Ex: 4.97 Ex5. Depth: Middle obs.

Midpoint

Class center. Relevance: Continuous. Ex: 0-10=5. Depth: Assume uniform.

Variability

Spread degree. Relevance: Interpretation. Ex: A high, B low. Depth: Dispersion measures.

Quartile Deviation

(Q3-Q1)/2. Relevance: Mentioned. Ex: Not studied. Depth: Interquartile.

Standard Deviation

Sqrt variance. Relevance: Later. Ex: Not in chapter. Depth: Root mean sq dev.

Measure of Central Tendency

Representative value. Relevance: Base for dev. Ex: Mean 53. Depth: Rough center.

Tip: Absolute for distance; N=sum f. Depth: No negatives. Errors: Forget abs. Historical: Bowley quote. Interlinks: Ch5. Advanced: Variance. Real-Life: Scores analysis. Graphs: Figs 13.1-2. Coherent: Center → Scatter.

Additional: Sum devs from mean=0. Pitfalls: Signed sum vanishes.

30 Questions & Answers - NCERT Based (Class 11) - From Exercises & Variations

Based on chapter examples. Part A: 10 (1 mark short), Part B: 10 (4 marks medium), Part C: 10 (8 marks long). Answers point-wise, numerical stepwise with MathJax.

Part A: 1 Mark Questions (10 Qs - Short from Illustrations & Variations)

1. What is dispersion?

1 Mark Answer:

Scatter around center

2. Range formula?

1 Mark Answer:

Max - Min

3. Why absolute in MD?

1 Mark Answer:

Signed sum=0

4. MD notation?

1 Mark Answer:

MD(a)

5. For ungrouped, n=?

1 Mark Answer:

Number of obs

6. Batsman A range?

1 Mark Answer:

7. Median for odd n?

1 Mark Answer:

$$(\frac{n+1}{2})^{th}$$

8. N in grouped?

1 Mark Answer:

Sum f_i

9. Continuous uses?

1 Mark Answer:

Midpoints

10. cf for median?

1 Mark Answer:

>= N/2