Formula Review

Suppose we have a set of data with $n$ values, ordered from smallest to largest. If $n$ is odd, then the median is the data value at position $\frac{n+1}{2}$. If $n$ is even, then we find the values at positions $\frac{n}{2}$ and $\frac{n}{2}+1$. If those values are named $a$ and $b$, then the median is defined to be $\frac{a+b}{2}$.

$s=\sqrt{\frac{{\displaystyle \sum {(x-\overline{x})}^2}}{n-1}}$

Here, s is the standard deviation, $x$ represents each data value, $\overline{x}$ is the mean of the data values, $n$ is the number of data values, and the capital sigma ($\mathrm{\Sigma }$) indicates that we take a sum.

If $x$ is a member of a normally distributed dataset with mean $\mu$ and standard deviation $\sigma$, then the standardized score for $x$ is

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

If a line has slope $m$ and passes through a point $(x_0,y_0)$, then the point-slope form of the equation of the line is:

Suppose $x$ and $y$ are explanatory and response datasets that have a linear relationship. If their means are $\overline{x}$ and $\overline{y}$ respectively, their standard deviations are $s_x$ and $s_y$ respectively, and their correlation coefficient is $r$, then the equation of the regression line is: