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Statistical and non statistical questions

Video transcript

what I want to do in this video is think about the types of questions that we need statistics to address and the types of questions that we don't need statistics to address and we could call the ones where we need statistics as statistical statistical questions statistical questions and I'll circle the statistical questions in yellow and I encourage you to pause this video and try to figure this out yourself first look at each of these questions and think about whether you think you need statistics to answer this question or you don't need statistics whether these are statistical questions or not so I'm assuming you've given up a stat it not unless we can we can go through this together so this first question is how old are you so we're talking about how old is a particular person there is an answer here and we don't need any tools of statistics to answer this so this is not a statistical question how old are the people who have watched this video in 2013 now this is interesting we're assuming that multiple people will have watched this video in 2013 and if they're not all going to be the same age there's going to be some variability in their age so one person might be 10 years old another person might be 20 another person might be 15 so what answer do you give here did you give all of the ages but we want to get a sense of in general how old are the people so this is where statistics might be valuable we might want to find some type of central tendency an average a median age for this so this is absolutely a statistical question and you might already be seeing kind of a pattern here the first question we were asking about a particular person there was only one answer here there's no variability in the answer the second one we're asking about a trait of a bunch of people and there's variability in that trait they're not all the same age and so we're only statistics to come up with some features of the data set to be able to make some conclusions we might say on average the people who have watched this video in 2013 are 18 years old or 22 years old or the median is 24 years old whatever it might be do dogs run faster than cats so once again there many dogs and many cats and they all run at different speeds some dogs run faster than some cats and some cats run faster than some dogs so we would need some statistics to get a sense of in general or on average how fast do dogs run and then it may be on average how fast do cats run and then we could compare those averages or we can compare the medians in some way so this is definitely a statistical question once again we're talking about in general a whole population of dogs the whole species of dogs versus cats and there's variation and how fast dogs run and how fast cats run if we were talking about a particular dog and a particular cat well then there would just be an answer does does dog a run faster than cat B well sure that's that's not going to be a statistical question you don't have to use the tools of Statistics and this next question actually fits that pattern do wolves wait actually no this fits the pattern of the previous one do wolves weigh more than dogs so once again there are some very light dogs and some very heavy wolves so those wolves definitely way more than those dogs but there are some very very very heavy dogs and so what you would want to do here because we have variability in each of these is you might want to come with some central tendency on average what's the median wolf wait what's the average the mean wolf wait compare that to the mean dogs wait so once again since we're speaking in general about wolves not a particular role wolf and in general about dogs and we're trying to and there's variation in the data and we're trying to glean some numbers from that to compare this is definitely a statistical question definitely a statistical question does your dog way more than that wolf and we're assuming that we're pointing at a particular wolf so now this is the particular we're comparing a dog to a particular dog to a particular wolf we can put each of them on a weighing machine and come up with an absolute answer there's no variability in this dogs weight at least at the moment that we weigh it no variable in this wolf's weight at the moment that we weigh it so this is not a statistical question so I'll put an X next to the ones that are not statistical questions does it rain more in Seattle than Singapore so once again there's variation here and we would also probably want to notice it rain more in Seattle than say poor in a given year over a decade or whatever but regardless of those questions however we asked it in some years it might rain more in Seattle in other years it might rain more in Singapore or in if we just pick Seattle it rains a different amount from year to year in Singapore it rains a different amount in from year to year so how do we compare well that's where the statistics could be valuable there's variability in the data so we can look at the data set for Seattle and come up with some type of an average some type of a central tendency and compare that to the average the mean the mode whatever you want to the mode probably wouldn't be that useful here to Singapore so this is definitely definitely a statistical question definitely statistical what was the difference in rainfall between Singapore in Seattle and 2013 well these two numbers are known they can be measured both the rainfall in Singapore can be measured the rainfall and Seattle will can be measured and assuming that this has already happened and we can measure them then we can just find the difference so you don't need statistics here you can just you need you just need to find you just have to have both of these measurements and subtract the difference so not a statistical question in general will I use less gas driving at 55 miles an hour than 70 miles per hour so this feels statistical because it probably depends on the circumstance it might depend on the car or even for a given car when you drive at 55 miles per hour there's some variation in your gas mileage it might be how recent an oil change happened what the wind conditions are like what the road conditions are like of weather I mean there's you know exactly how you're driving the car are you turning are you going in a straight line and same thing for 70 miles an hour so when we're seeing in general there's variation in what the gas mileage is at 55 miles an hour and at 75 70 miles an hour so what you'd probably want to do is say well what's my average mileage when I drive at 55 miles an hour and compare that to the average mileage when I drive at 70 so because we have this variability in each of those cases this is definitely a statistical statistical question do English professors get paid less than math professors so once again some all English professors don't get paid the same amount and all math professor don't get paid the same amount some English professors might do quite well some might make very little same thing for math professors so we'd probably want to find some type of an average to represent the central tendency for for each of these so once again this is a statistical question this is a statistical question does the most highly paid English professor at Harvard get paid more than the most highly paid math professor at MIT well now we're talking about two particular individuals you could go look at their tax forms see how much each of them get paid and we I guess especially if we assume that this is in a particular year let's say let's just make it that way say in 2013 just so that we can remove some variability that they might make from year to year make it a little bit more concrete so if this was does the most highly paid English professor at Harvard get paid more than the most highly paid math professor at MIT in 2013 then you have an absolute number for each of these each of these people and then you could just compare them directly and so when we're talking about a particular year particular people then this is no longer a statistical question or it isn't a statistical question