# Statistics class 11 Notes Mathematics

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## CBSE Guide Statistics class 11 Notes

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## Statistics class 11 Notes Mathematics

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

1. Mean: $\overline x = {{{x_1} + {x_2} + ........ + {x_n}} \over n}$
2. 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.
3. Measures of Dispersion, Range  and Mean Deviation
4. Variance and Standard Deviation
5. 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 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.

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