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in this video we're going to talk about another way of visualizing data called the histogram histogram which is a very fancy word for a not so fancy thing and I think it's probably fair to say that the histogram is the most used way of representing statistical data and let me just show you how to figure out a histogram for some data and I think you're going to get the point pretty easily so I have some data here and I want to represent it with a histogram and we're going to see is how frequent are each of these numbers and in order to figure that out let me just write the numbers down and let me just categorize them in their respective buckets so I have a 1 here so I have 1 1 right there I have a 4 let me put it so I want to leave space for the 2 the 3 and put a 4 there I have a 2 that - I have a 1 let me put that one on a stack right above that one I have a 0 let me put the 0 to the left of the one I want to put them in order I have a to another - let me stack that above my first - I have another one let me stack that above my other two ones I have another 0 let me stack it there I have another one another one right there then I have another to another to another one another one I have two more zeroes 0 0 I have two more twos two more twos I have a 3 I have a 3 I have two more ones two more ones another three and then I have a 6 so no fives and then I have a 6 and that space right there was unnecessary but right here I've listed I've just rewritten these numbers and I've essentially categorized them now what I want to do is calculate how many of each of these numbers we have so let me go down here so I want to look at the frequency of each of these numbers the frequency of each of these numbers so I have one two three four zeros I have one two three four five six seven ones I have 1 2 3 4 5 2 's I have one two threes I have one four and six and sorry and one six so we could write it this way we could write the number the number and then we can have the frequency the frequency and so I have the numbers 0 1 2 3 4 we could even throw 5 in there although 5 has a frequency of 0 and we have a 6 so the 0 showed up four times in this data set one showed up seven times in this data set two showed up five times two showed up five times three showed up two times four showed up one time five didn't show up and six showed up one times all I did is I counted this data set I'm I did this first but you could say how many times do I see a zero I see it one two three four times how many times do I see a one one two three four five six seven times that's what we mean by frequency now a histogram is really just a plot a kind of a bar graph plotting the frequency of each of these numbers it's going to look a lot like this original thing that I drew so let me draw some axes here so the different buckets here are the numbers and that worked out because we're dealing with very clean integers that tend to repeat if you're dealing with things that are more that aren't just you know that the exact number doesn't repeat oftentimes people will put the numbers into buckets or ranges but here they fit into nice little bucket so you have the numbers 0 1 2 3 4 5 & 6 this is the actual numbers and then on the vertical axis we're going to plot the frequency we're going to plot the frequency so 1 2 3 4 5 6 7 so that's 7 6 5 4 3 2 1 so 0 shows four times so we'll draw a little bar graph here zero shows up four times just like that zero four toes up four times that is that information right there one shows up seven times one shows up seven times so I'll do a little bar graph one shows up seven times just like that one shows I'm going to make it a little bit straighter than that one shows up seven times one shows up seven times two - other than a different color two shows up five times two shows up five times bar graph go all the way up to five two shows up five times three shows up two times three shows up exactly two times here we have one three two three four shows up one time here so four shows up one time five doesn't show up at all five doesn't show up at all so we could even need a little doesn't even get any height there and then finally finally six shows up six shows up one time so I'll do six showing up one time what I just plotted here this is a histogram this right here is a histogram very fancy word but I think you will agree it's a fairly simple idea figure out the frequency of each of these numbers and then plot the frequency of each of these numbers and you get yourself a histogram