Contemporary Mathematics

# Formula Review

## 8.3Mean, Median and Mode

Suppose we have a set of data with $nn$ values, ordered from smallest to largest. If $nn$ is odd, then the median is the data value at position $n+12n+12$. If $nn$ is even, then we find the values at positions $n2n2$ and $n2+1n2+1$. If those values are named $aa$ and $bb$, then the median is defined to be $a+b2 a+b2$.

## 8.4Range and Standard Deviation

$s=∑ (x-x¯)2n-1s=∑ (x-x¯)2n-1$

Here, s is the standard deviation, $xx$ represents each data value, $x¯x¯$ is the mean of the data values, $nn$ is the number of data values, and the capital sigma ($ΣΣ$) indicates that we take a sum.

## 8.6The Normal Distribution

If $xx$ is a member of a normally distributed dataset with mean $µµ$ and standard deviation $σσ$, then the standardized score for $xx$ is

$z=x-µσ.z=x-µσ.$

If you know a $zz$-score but not the original data value $xx$, you can find it by solving the previous equation for $xx$:

$x=µ+z×σ.x=µ+z×σ.$

## 8.8Scatter Plots, Correlation, and Regression Lines

If a line has slope $mm$ and passes through a point $(x0,y0)(x0,y0)$, then the point-slope form of the equation of the line is:

$y=m(x-x0)+y0y=m(x-x0)+y0$

Suppose $xx$ and $yy$ are explanatory and response datasets that have a linear relationship. If their means are $x¯x¯$ and $y¯y¯$ respectively, their standard deviations are $sxsx$ and $sysy$ respectively, and their correlation coefficient is $rr$, then the equation of the regression line is:

$y=r(sysx)(x-x¯)+y¯.y=r(sysx)(x-x¯)+y¯.$
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