Quant · Modern Maths

Statistics

2 sub-topics · 13 lessons · 67 questions · 7 PYQs

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Mean, Median and Mode9 lessons · 51 questions · 7 PYQs

Range, Variance and Deviation4 lessons · 16 questions

Formula sheet

Range
$\text{range}=\max-\min$
Coefficient of variation
$\text{CV}=\frac{\sigma}{\bar x}\times100\%$
Variance of the first n natural numbers
$\text{Var}(1,2,\dots,n)=\frac{n^2-1}{12}$
Mean of raw and grouped data
$\bar x=\frac{\sum x_i}{n},\quad \bar x=\frac{\sum f_ix_i}{\sum f_i}$
Effect of a linear change on mean and spread
$y=ax+b\ \Rightarrow\ \bar y=a\bar x+b,\quad \sigma_y=|a|\sigma_x,\quad \sigma_y^2=a^2\sigma_x^2$
Variance and standard deviation
$\sigma^2=\frac{1}{n}\sum(x_i-\bar x)^2=\frac{\sum x_i^2}{n}-\bar x^2,\qquad \sigma=\sqrt{\sigma^2}$
Expected value and the mean of 1 to N
$E(X)=\sum x_iP(x_i);\quad \text{mean of }1..N=\frac{N+1}{2}$
Correcting a misread observation
$\text{corrected mean}=\bar x+\frac{b-a}{n};\quad \sum x^2=n(\sigma^2+\bar x^2)$