Question

statistics formula and some examples​

Answer 1

For the following formulas, assume that Y is a linear transformation of the random variable X, defined by the equation: Y = aX + b. ... Variance of a linear transformation = Var(Y) = a2 * Var(X). Standardized score = z = (x - μx) / σx. t statistic = t = (x - μx) / [ s/sqrt(n) ]

Answer 2

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$\bigstar$$\underline{\sf{\orange{Statistics}}}$

Statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution. In short, Statistics is associated with collecting, classifying, arranging and presenting numerical data.

$\bigstar$$\underline{\sf{\green{Most\:common\:statistical\:formula;}}}$

The most common calculated statistical values are mean, median, and mode.

$\bigstar$$\underline{\sf{\pink{Examples\:of\:Statistical\:Formula}}}$

$\sf{Mean}$ = $\sf{\frac{Observation\:given}{Total\:number\:of\:observations}}$

$\sf{Median}$ = $\sf{L\:+}\frac{(n/2)\:-B}{G}\:×\:w$

Where,

• L is the lower class boundary of the group containing the median
• n is the total number of values
• B is the cumulative frequency of the groups before the median group
• G is the frequency of the median group
• w is the group width

$\sf{Mode}$ = $\sf{\frac{f_{m}\:-\:f_{m-1}}{(f_{m}\:-\:f_{m-1})\:+\:(f_{m}\:-\:f_{m+1})}}$

Where,

• L is the lower class boundary of the modal group
• fm-1 is the frequency of the group before the modal group
• fm is the frequency of the modal group
• fm+1 is the frequency of the group after the modal group
• w is the group width

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