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for senior project richard is researching how much money a college graduate can expect to earn based on his or her major he finds the following interesting facts basketball superstar Michael Jordan was a geology major at the University of North Carolina there were only three civil engineering majors from the University of Montana they all took the exact same job at the exact at the same company earning the same salary of the 35 finance majors from Wesleyan University 32 got high-paying consulting jobs and the other three were unemployed for geology majors from the University of North Carolina the median income will likely be and we have some options here less than equal to or greater than the mean and then we have to answer the same question for civil engineering majors from Montana the median income Oh actually the dues were both about median the median income will be and we compare it against the mean and then from flat for finance majors from Wesleyan we're going to compare the median income to the mean so to visualize this a little bit more I've copy and pasted this exact same problem onto my scratch pad so here it is I can now write on this so let's think about each of these for geology majors from UNC the median income will be will likely be how will that compare to the mean well what did they tell us about UNC they tell us that Michael Jordan was a geology major at the University of North Carolina so what is the what will the distribution of salaries probably look like so if we're thinking about the University of North Carolina it probably looks something like this and I'm going to do a very very rough a very rough distribution right over here and let's say that this salary this would be a salary of zero and let's say that this is a salary of I don't know let me put a salary of 50k here I'll do this in thousands this let's say this is a hundred thousand right over here and then you have Michael Jordan who is actually I'll do a little gap here because he's so far up I don't know exactly what he was making but it was definitely in the tens of millions of dollars a year so Michael Jordan is way way way way up here so if you were to make a histogram or a plot of all of the salaries because okay well you know maybe we have if you put all of the all of the folks from geology majors at University of North Carolina well there's probably especially right when they graduated there's probably you know one two three I could keep doing it a bunch of people may be making 50k maybe some people making a little bit more maybe some people up here maybe some people there some people there some people there like there may be someone's making 100k maybe someone so maybe it's a couple of people up there maybe someone isn't making anything maybe they did they weren't able to find a job and then of course you have Michael Jordan up here making you know ten million dollars or twenty million dollars or something like that so when you have a situation like this where you have this outlier of Michael Jordan it's going to put it's going to put that you one way I think about it kind of tugs on the mean it wouldn't affect the median because remember the median is the middle value so it doesn't matter how high this number is you could make this a trillion dollars it's not going to change what the middle value is the middle value is still going to be the same middle value you could move this anywhere around in this range it's not going to change the median but the mean will change if this becomes really really astronomically high it will distort the actual mean here actually would distort it a good bit so for the geology majors from UNC the median income is going to be lower than the mean because Michael Jordan is pulling the mean up so let me fill that in so for geology majors from UNC the median will be less than the mean now let's think about the other ones for civil engineering majors from Montana the median income will be blank the mean well they tell us there were only three civil engineering majors from the University of Montana they all took the exact same job at the same company earning the same salary so let's say all three of them earned $50,000 let's say that's their salary so you have if you were to if you were to calculate the mean it would be 50 plus 50 plus 50 over 3 which of course is 50 that would be the mean if you wanted the median you list the salaries in order and then you take the middle one well the middle one is 50 so in this case the median is equal to the mean so let's fill that at that in median is equal to the mean and then finally let's go back to my scratch pad whoops let me go back to my scratch pad here for finance majors from Wesleyan the median income will be blank the mean so let's think about this distribution here so here we have 35 out of the 35 32 got high-paying consulting jobs so let's say that they were making you know they were making six figures so so the distribution might look something like this where if this is zero and this is let's say this is 50k and let's say that this right over here is $100,000 a year so 32 got high-paying consulting job so you might have 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 so the distribution for the people who got the jobs might look something like that but there were three people who were unemployed so let's say they got no income so you have 1 2 3 so this is now you have 3 outliers like the Michael Jordan situation but instead of them being very high they are very low so they're going to pull the mean lower they're not going to if these were 0 or if these were 50 or if these were over here they're not going to affect the median the middle number is still going to be the same but they are going to pull down the mean so here I would say that the median income will likely be higher will likely be greater than the mean because because the mean is going to get pulled down by these outliers these three people not making anything so let's fill that out for finance majors from Wesleyan the median income will likely be greater than the mean and let's check our answer and we got it right