hey and here's my ap statistics 10 minute review here i'm going to try to keep it to 10 minutes um this is obviously not every single thing you need to know in the class but it's trying to be a give a big highlight and some important tips for the ap exam so first off first unit describing data you're going to usually be asked to ask a question on the frq that's asking about you know something box plots dot plots histograms stem plots maybe even um yeah those are the main plots when you're asked to describe that make sure you hit up the four points the shape that is whether it's skewed or not whether it's unimodal or bimodal the spread that could be describing the range the iqr the standard deviation or make sure you know what those are the center which could be the mean or the median and finally outliers anything beyond two standard deviations of the mean or outside the 1.5 iqr fence make sure you know how to do all of those things as well as the five number summary which is the min max q1 median and q3 when you're analyzing scatter plots and you're looking at them they want you to show strength of the association that's whether strong moderate or weak the direction whether it's positive or negative positive meaning was one variable goes up the other goes up negative meaning the opposite one goes up the other goes down the shape whether it's linear curved and then any outliers anything far away from the general trend you want to make sure you hit those points when you're asked to describe data for those kinds of um situations collecting data so here is where we talk about sampling and bias and you know how we do up experiments versus observational studies the different methods of sampling you got simple random sample that's where you just take everyone and you randomly pick from the entire population they're stratified where you're where you're grouping them into groups first and then picking from within the group okay so what you're doing is you're stratifying by a variable you think that is you know important to separate because you want to make sure for example you might want to know you know i want to get men and women and i want to you know make sure i get an even number of men and women so i may separate them first and randomly select from those two groups as opposed to cluster where things are naturally grouped i'm going to randomly pick one of the groups and sample everyone within that group i don't get everyone from every group i for example like in clustering you may say if you're going to sample at your school you may randomly pick a classroom and then sample everyone in that classroom okay as opposed to stratifying which you would be grouping maybe by 9th 10th 11th and 12th graders and randomly selecting from within that group that's the difference between stratified and clustered convenience is just something that you do that's easy for you to do that is you grab people who are walking into school or you just do something that's that's it's not it's not a random or not fully random systematic is something like you take every tenth item or every fifth item or something like that something you just kind of systematically do for your sampling okay now when you're collecting data and you're sampling or you're doing surveys there are various kinds of bias that can be involved there's non-response bias that's where people who don't answer might have a different different makeup or different behavior than the people who do answer there's under coverage where you're sampling a group of people but you're not necessarily grabbing from the whole population okay uh voluntary responses people who do respond tend to have a very very strong opinion like people who leave yelp reviews usually people who love it or usually people who hate it it's not usually like the mediocre people would just be like it was fine response is the way that the the study is done that may introduce um the response to lean in one way um as an example it's not that's different from the wording bias which is how the question is word the response bias is like for example if you have if i'm asking you have you ever broken the law and it's an anonymous survey as opposed to you randomly get selected you go talk to a police officer and they ask you have you ever broken the law you may answer the question a little bit differently because of the situation not because the way it was worded but because of the situation wording bias is the way the questions are asked may affect the way people lean one way or the other now when you're asked about bias about one of these things be specific about how the bias affects it you want to say something like in my example with the police officer i might say well the police officer is intimidating and a person might be more inclined to lie and say they haven't broken the law when in fact they have okay so they're more likely to say no because of that so you want to be specific on how the bias actually affects the answer to the the situation there don't just say that the presence of the police officer would cause bias or response bias you need to be more specific about how it affects the response okay and then experiment versus observational study experiments are the only way we do causality okay we always we can only show association by observational studies and the difference between experiments and observational studies is in experiments you are randomly forcing people to or you know the things under treatments and you're randomly assigning them into treatments you are not letting themselves select for example suppose i want to know if smoking causes cancer okay observational studies i study the people who have smoked and the study people haven't smoked and i and i observe the incident rates of cancer that's observational i did not force them to smoke or not experiment would be like i take two random groups of people i force this group of people to smoke i force this group of people to not smoke and then i compare their results okay now experiments can show causality more directly a lot of the times experiments are immoral like that would be a very immoral and illegal experiment to do to force these people to smoke and force these people to not smoke that would be you know inappropriate and illegal and unethical ultimately to do so that's why sometimes we only use observational studies because we cannot perform experiments for whatever reason probability this is a tough topic sometimes so i'm going to try and there's a lot and deep in here so make sure you feel good about the probability but you always get a probability frq so first when asked to describe a distribution you need to identify the name of the distribution as well as the parameters associated with that for example if i ask you if you know something is a binomial distribution know the conditions what is a binomial distribution but it's described by the number of trials n and by the probability p those parameters are given to you on your formula sheet if you want to look at them but it's good for you to know geometric distribution is described by the probability p of failure or the first success or failure depends on what you define success and failures are not really like they have no specific context specific meanings they're driven by the context of the uh what you're trying to count basically so normal distribution is always described by a mean and a standard deviation so if i'm asking you to describe what is the distribution don't just tell me the name don't just say binomial geometric or normal tell me the parameters these parameters and those values associated with that distribution make sure you understand the difference between a sampling distribution and a population distribution okay like a sample mean or something like that make sure you know conditional probability right that's if something is conditioned on an event and what that means and what independence ultimately means as relation to conditional probability and then here i want to hit up because i know this is an area that a lot of students struggle with so i want to focus on this know how they're different transformations can affect the mean and standard deviation for example if i take a random variable multiply by constant the mean and standard deviation both multiply by that constant as opposed to taking a random selection so so for example suppose i know the distribution weight of like um a marble has a weight of a mean mu and a standard deviation blah and i take the weight of one marble and multiply by 10 then the mean and standard deviation multiply by 10. however in contrast if i take 10 random marbles all with those same distribution then the mean is n times that mean and the standard deviation gets multiplied by the square root of n okay there's a difference between that sorry i didn't i didn't mean the mean weight i meant if i took 10 marbles and added the weight of every marble but each marble was independent and had its own distribution then the standard deviation doesn't get multiplied by n it gets multiplied by the square root of n there's a difference between me randomly selecting 10 things versus me randomly selecting one thing and multiplying it by 10. so make sure you understand that difference and when you add two random variables to if they're the means always add so you just add the means the mean of x plus the mean of y the standard deviation adds by kind of like this some people call the pythagorean theorem of random variables is basically you add the square root of the square of the standard deviations now that's only if x and y are independent you can't just do that for any two random variables you add it must be explicitly stated that x that those two random variables are independent if you do that the mean ones you can always add regardless if they're independent or not okay hypothesis testing i have another video where i go through all the different hypothesis testings but if you're performing a hypothesis test or a confidence interval here's the name here's the things you want to do you want to state the conditions and show how they're being met in the question they're usually pretty short to show but make sure you understand the three conditions for all of the the normal distribution issue um uh ones and then the conditions for um uh chi squared there's always three conditions it's the random independence and then for you know the z or t tests it's normal conditions and for chi-squared it's the expected counts but know how they're different for proportions for sample means for the chi-square that other video kind of goes through that make sure you name the test specifically i don't know how many times you just tell me not the name of the function on the calculator is okay but i would prefer and it's better if it's very clear you identify whether it's a one or two sample whether it's a proportion versus a sample mean whether it's z versus t and then for chi-square that's a separate thing you can just say chi squared for that okay name that specifically because the calculator functions say like one sample one sample is not clear necessarily i prefer you say one sample mean because it is technically sample mean not just a sample proportions are always samples also what we call it so use things like one prop z test or two sample mean t test or something like that make sure you state the null and alternative hypothesis show both the test statistic and the p-value even when you're using a calculator i know your conclusion is just based on the p-value but show the test statistic as well as the p-value and then write an appropriate conclusion in context for a confidence interval it's basically identical except that rather than um showing the p-value you're going to show what the confidence interval is okay instead and then write an appropriate conclusion for that like i said i'll put a link in the description below to that other video on hypothesis testings because that one's a little bit longer to understand if you're having trouble identifying it okay so those are the main ideas on the frqs and the topics that you should look at obviously it's not exhaustive but hopefully it gives you a pretty good idea of the things that you should be doing