Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2024-25, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Install Now

CBSE Mathematics Chapter 15 Statistics class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Statistics class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on Chapter 15 Statistics class 11 Notes Mathematics are also available for download in CBSE Guide website.

CBSE Guide Statistics class 11 Notes

CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 11 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.

Statistics class 11 Notes Mathematics

Download CBSE class 11th revision notes for Chapter 15 Statistics class 11 Notes Mathematics in PDF format for free. Download revision notes for Statistics class 11 Notes Mathematics and score high in exams. These are the Statistics class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

Download Revision Notes as PDF

CBSE Class 11 Mathematics
Revision Notes
Chapter-15
Statistics class 11 Notes Mathematics

Mean: $\overline x = {{{x_1} + {x_2} + ........ + {x_n}} \over n}$
Median: If the number of observations $n$ is odd, then median is ${\left( {{{n + 1} \over 2}} \right)^{th}}$ observation and if the number of observations $n$ is even, then median is the mean of ${\left( {{n \over 2}} \right)^{th}}$ and ${\left( {{{n + 1} \over 2}} \right)^{th}}$ observations.
Measures of Dispersion, Range and Mean Deviation
Variance and Standard Deviation
Analysis of Frequency Distributions

Measures of dispersion Range, Quartile deviation, mean deviation, variance, standard deviation are measures of dispersion.
Range = Maximum Value – Minimum Value
Mean deviation for ungrouped data
$M.D.\ (\bar{x})=\frac{\sum{|{{x}_{i}}-\bar{x}{{|}_{{}}}}}{n}$
Mean Deviation from Median for ungrouped data
$M.D.\ (M)=\frac{\sum{|{{x}_{i}}-M{{|}_{{}}}}}{n}$
Mean deviation for grouped data
$M.D.\ (\bar{x})=\frac{\sum{{{f}_{i}}|{{x}_{i}}-\bar{x}{{|}_{{}}}}}{N}$
Mean Deviation from Median for grouped data
$M.D.\ (M)=\frac{\sum{{{f}_{i}}|{{x}_{i}}-M{{|}_{{}}}}}{N}$ where N = $N=\sum\limits_{{}}^{{}}{{{f}_{i}}}$
Variance and standard deviation for ungrouped data
Variance: ${{\sigma }^{2}}=\frac{1}{n}\sum\limits_{{}}^{{}}{{{({{x}_{i}}-\bar{x})}^{2}}}$
Standard deviation: ${{\sigma }^{2}}=\sqrt{\frac{1}{n}\sum\limits_{{}}^{{}}{{{({{x}_{1}}-\bar{x})}^{2}}}}$
Variance and standard deviation of a discrete frequency distribution
Variation: ${{\sigma }^{2}}=\frac{1}{N}\sum\limits_{{}}^{{}}{{{({{x}_{i}}-\bar{x})}^{2}}}$
Standard deviation: ${{\sigma }^{2}}=\sqrt{\frac{1}{N}\sum\limits_{{}}^{{}}{{{f}_{i}}{{({{x}_{1}}-\bar{x})}^{2}}}}$
Variance and standard deviation of a continuous frequency distribution

(i) If ${{{x_i}} \over {{f_1}}};$ $i$ = 1, 2, 3, ………., $n$ is a continuous frequency distribution of a variate X,

then ${{\sigma }^{2}}=\frac{1}{N}\sum\limits_{{}}^{{}}{{{f}_{i}}({{x}_{i}}-\bar{x}}{{)}^{2}}$

(ii) If ${x_1},{x_2},.......,{x_n}$ be the $n$ given observations with respective frequencies

${f_1},{f_2},.......,{f_n}$ , then $\sigma =\frac{1}{N}\sqrt{N\sum\limits_{{}}^{{}}{{{f}_{i}}x_{i}^{2}}-(\sum\limits_{{}}^{{}}{{{f}_{i}}{{x}_{1}}{{)}^{2}}}}$ , where N = $\sum {{f_1}}$

(iii) If ${d_i} = {x_i} - {\rm{A,}}$ where A is assumed mean, then ${\sigma ^2} = {1 \over {\rm{N}}}\sum {{f_i}d_i^2 - {{\left( {{{\sum {{f_i}{d_i}} } \over {\rm{N}}}} \right)}^2}}$

(iv) If ${u_i} = {{{x_i} - {\rm{A}}} \over h},$ where $h$ is the common difference of values of $x,$ then

${\sigma ^2} = {1 \over {\rm{N}}}\left[ {\sum {{f_i}u_i^2 - {{\left( {{{\sum {{f_i}{u_i}} } \over {\rm{N}}}} \right)}^2}} } \right]$

Analysis of frequency distribution with equal means but different variances: If the S.D. of group A < the S.D. of group B, then group A is considered more consistent or uniform.
Ananlysis of frequency distribution with unequal means: In this case we compare the coefficient of variation [Coefficient of variation (C.V. = The series having greater coefficient of variation is said to be more variable than the other.
Variance of the combined two series: ${\sigma ^2} = {1 \over {{n_1} + {n_2}}}\left[ {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right]$
where ${{n_1}}$ and ${{n_2}}$ are the sizes of two groups, ${\sigma _1}$ and ${\sigma _2}$ are the S.D. of two groups, ${d_1} = \overline a - \overline x$ , ${d_2} = \overline b - \overline x$ and $\overline x = {{{n_1}\overline a + {n_2}\overline b } \over {{n_1} + {n_2}}}$

Statistics class 11 Notes

CBSE Revision notes (PDF Download) Free
CBSE Revision notes for Class 11 Mathematics PDF
CBSE Revision notes Class 11 Mathematics – CBSE
CBSE Revisions notes and Key Points Class 11 Mathematics
Summary of the NCERT books all chapters in Mathematics class 11
Short notes for CBSE class 11th Mathematics
Key notes and chapter summary of Mathematics class 11
Quick revision notes for CBSE exams

CBSE Class-11 Revision Notes and Key Points

Statistics class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

To download Statistics class 11 Notes, sample paper for class 11 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Create Now

myCBSEguide

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Install Now

Statistics class 11 Notes Mathematics

myCBSEguide App

CBSE Guide Statistics class 11 Notes

Statistics class 11 Notes Mathematics

Download Revision Notes as PDF

Statistics class 11 Notes

CBSE Class-11 Revision Notes and Key Points

Test Generator

myCBSEguide

Related Posts

Leave a Comment