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Hi I'm Adrienne Hill and Welcome to Racecourse Statistics We've spent out a lot of time talking about data visualization and different kinds of frequency plots--like dot-plots and histograms--thattell us how frequently things occur in data we actually have But so far in this series the data we have talked about usually isn't ALL the data that exists If I want to know about student loan dentin America I am definitely not going to ask over 300 million Americans I'm lazy like that But maybe I can find the time to ask 2000of them Sample sand the shapes they give foreshadows of what all the data would look like We collect samples because we think thallium us a glimpse of the bigger picture They'll tell us something about the shape of all the data Because it turns out we can learn almost everything we need to know about data from its shape Intro Picture a histogram of every single persons height Now imagine the bars getting thinner and thinner and thinner as the bins get smaller and smaller Till they are so thin that the outline four histograms looks like a smooth line since this is a distribution of continuous numbers And there's an infinite chance of heights I am 167642 and on and on meters tall If we let our bars be infinitely small beget a smooth curve also known as the distribution of the data A distribution represents all possible values for a set of data and how often those values occur Distributions can also be discrete Like the number of countries people have visited That means they only have a few set values--thatthey can take on These distributions look a lot more like the histograms were used to seeing Like a histogram the distribution tells us about the shape and spread of data We can think of distributions as a set of instructions for a machine that generates random numbers Lets say it generates the number of leave son a tree You may well be wondering why we'd have tree-leaf-number generating machine The idea here is that EVERYTHING can generate data Its not just mechanical stuff Its leaves and animals and even people The distribution is what specifies how the knobs and dials on our machine are set Once the machine is set every time Theresa new tree the machine pops out a random number of leaves from the distribution It won't be the same number each time though That's because its a random selection based on the information the knobs and dials tell us about our distribution of leaves When we look at samples of data generated by our leaf machine were trying to guess the shape of the distribution and how that machines knobs and dials are set But remember samples of data are not all the data so when we compare the shapes of two samples of data were really asking whether the same distribution--these two machine settings--could have produced these two different--butsorta similar--shapes If you got an especially expensive electricity bill last month you may want to look at the histogram of your average daily energy consumption this month and...
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