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Formula Review

8.3 Mean, 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.

8.4 Range 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.

8.6 The 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


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


8.8 Scatter 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:


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:

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