# A New Formula Sheet for the AP Statistics Exam

Updated: Feb 21, 2021

Recently, College Board released the new Course and Exam Description, a 263 page document that clearly outlines the content expectations for the course. This is all fine and dandy, but the experienced AP Stats teachers knew what else was coming: __A NEW FORMULA SHEET! __

Check out this video that walks students through every single formula on the new formula page. This video is part of the Stats Medic AP Statistics Exam Review Course.

If you are an experienced AP Statistics teacher, you might want to know exactly what is different about this new formula sheet as compared to the previous version. Read on!

**Section I: Descriptive Statistics**

**Section I: Descriptive Statistics**

The formula for the pooled standard deviation is no longer included. Hooray!

The equation of the least-squares regression line is now in y = a + bx (as it should be), rather than the y = b0 + b1x form.

The formula for the

*y-*intercept is in a different form (solved for the mean of y, not the*y-*intercept).The “hard” formula for the slope is no longer included and the formula for the standard error of the slope has been moved to the sampling distribution and inference section.

**Section II: Probability and Distributions**

**Section II: Probability and Distributions**

Most of the formulas in this section have been arranged in a table.

The formulas for binomial and geometric probability in the new formula sheet use

*P*(*X*=*x*) instead of*P*(*X*=*k*) and replace all instances of*k*with*x*. In the*P*(*X*=*x*) notation, upper case*X*represents the random variable and lower case*x*represents a particular value of the random variable.**Formulas for the geometric distribution, including the mean and standard deviation, are now included.**Formulas for the sampling distributions have been moved to Section III.

**Section III: Sampling Distributions and Inferential Statistics**

**Section III: Sampling Distributions and Inferential Statistics**

In the formulas for a standardized test statistic and a confidence interval, “standard

*deviation*of statistic” has been replaced with “standard*error*of statistic.”

Standard errors are designated with the notation

*s*rather than SE like many of us are used to.The formula for the standard error of the difference in proportions (when

*p*1=*p*2 is assumed) now includes information about how to calculate the combined (pooled) proportion.

Notice that the new formula sheet uses upper case X instead of lower case x.

The formulas for the sampling distribution of a sample slope are now included. In the previous formula sheet, only the formula for the standard error of the slope was included (in Section I).

Note the new formulas below the standard error of the slope, which include the formula for the standard deviation of the residuals

*s*and the standard deviation of*x*,*sx*.There is a new note at the end of the formula sheet briefly describing the difference between the standard deviation and the standard error. In short, we almost always use the standard error because we are using data from the sample(s) to estimate variability. If we happen to know the standard deviation of the sampling distribution (like in the one-sample

*z*test for*p*), use the standard deviation, not the standard error.