8.10.4: Formula Review

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Formula Review

8.3 Mean, Median and Mode

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 $n + \frac{1}{2}$ . 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 $\frac{a + b}{2}$ .

8.4 Range and Standard Deviation

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

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

8.6 The Normal Distribution

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

$z = \frac{x - µ}{σ} .$

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

$x = µ + z \times σ .$

8.8 Scatter Plots, Correlation, and Regression Lines

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:

$y = m (x - x_{0}) + y_{0}$

Suppose $x$ and $y$ are explanatory and response datasets that have a linear relationship. If their means are $\bar{x}$ and $\bar{y}$ 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:

$y = r (\frac{s_{y}}{s_{x}}) (x - \bar{x}) + \bar{y} .$

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Formula Review

8.3 Mean, Median and Mode

8.4 Range and Standard Deviation

8.6 The Normal Distribution

8.8 Scatter Plots, Correlation, and Regression Lines