Intro to Statistics- Guide to Assignment 3



assignment 3 preview question 1 for each of the datasets described below decide which measure of central tendency would be most appropriate and explain your choice consider the scale of measurement for each variable and the likely distribution of the observations so here are some big words and they are key words so let me underline those measure of central tendency what do we mean by that we're talking about the three averages very mean median and mode and then how about scale of measurement what does that refer to that reports to the four types of data namely nominal ordinal interval and ratio and then when we're talking about distribution we're talking about normal or skewed so we want to consider all these things to be able to figure out what would be the most appropriate central tendency mean median and mode and explain by talking about the scale of measurement and distribution if applicable right so in previewing this let's look at the first one together the scores of five hundred great six students on the math sub test right so here we have some math sub tests so is this going to be categorical or continuous it would be continuous right then we ask the question is this interval or ratio and in anytime you have a standardized test we're talking about the data being normal our ratio let me start over assignment 3 preview assignment three preview question one for each of the datasets described below decide which measure of central tendency would be most appropriate and explain your choice consider the scale of measurement for each variable and the likely distribution of the observations first before we proceed there are some big fancy words that we've talked about before one of them is measure of central tendency so when we talk about measure of central tendency we're talking about mean median or mode and then here you have another fancy raised scale of measurement and scale of measurement is namely the four types of variables nominal ordinal interval or ratio and then the likely distribution distribution can be either normal or skewed so what we want to figure out is which of the three measures of central tendency mean median or mode which a report for these data listed here so we want to consider first of all what type of variable they are and appropriate what type of distribution it is and see which measure of central tendency would be the appropriate measure set of central tendency to report so what would be helpful here is to look at the graph in the previous slide to kind of follow along and use that as a guide so in question a says the scores of 500 grade 6 students on a math sub test of an m-80 or standardized score so whenever you have standardized scores it's going to be numerical not categorical right or continuous so it's continuous data and more specifically is this interval or ratio sanitize tests ratio and sanitize tests are also normally distributed which would be your next question to think about the distribution is that it's going to be normal so let me have the data that is continuous ratio and normal where do you end up as far as the measure of central tendency to report it's going to be the mean so similarly then you want to consider these additional variables and the last question is which average is defined as a value that has 50% of the cases below it this is not a variable but it's a question that helps us to understand the concept of the various three averages so see if you can give it some thought so in question two then it says to report your answer to two decimal places Group a has these scores and group B also these scores in questions a in these has to report the mean the median and the mode of each group group a and Group B and then in question C says what is the most appropriate measure of central tendency in each group and why so first let's calculate the mean median and mode in both groups for the mean you want to add these numbers up and total them okay and then divided by the number of scores in this case is one two three four five six seven eight scores right so you want to total them and divide by eight to get your mean how do you get the meet median in order to get the median you want to align these numbers up in order starting with number five and listing it with number five seven and seven again right and in that sequence and go right to the middle right because that's how median is defined and in the case that you can't reach or the middle is not a particular score but in between those two scores and you want to take the mean of those two scores in the middle for the mode is the most popular answer or the most commonly occurring score so in this case in Group A you see that seven happens twice but no other numbers occur more than once so the mode there would be seven so once we have the mean median and mode reported through both groups then in question three or see it says what is the most appropriate measure of central tendency in each group what you're looking for then is to look at the mean and the median in with your results so if your mean and your median are equal we would say it's normally distributed but in the case that they're different then they're skewed right so again if the mean and median are the same if they're equal we would say it's normal and if they're not the same then we say it's skewed now we know that it's skewed to the positive side or the negative side depending on the size right whether the mean is greater or less than the median so you want to look at your notes in previous slides to figure out whether if there's a difference between the mean and the median depending on the size whether it's positive or negatively skewed in question three it's true or false and if the statement is false see if you can correct them so here are statements question a or statement a that mean is the most frequently occurring average is that true or false and if incorrect or false make that correction the second statement says in a distribution with a positive skew the median has a higher value than the mean true or false and if false correct the statement you know normal distribution the mean the median and the mode have the same value true or false and lastly the median has 50% of the cases below it only in a normal distribution true or false and a false make that into a correct statement

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