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# Histograms

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- In this video we're going to talk about another way of
- visualizing data called the histogram, which is a very
- fancy word for a not so fancy thing.
- I think it's probably fair to say that the histogram is the
- most used way of representing statistical data.
- 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.
- What 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, let me just categorize them in their
- respective buckets.
- So I have a 1 here.
- I have a 4, so I want to leave space for the 2, the 3, and
- put a 4 there.
- I have a 2.
- I have a 1.
- Let me put that 1 on a stack right above that 1.
- I have a 0-- let me put the 0 to the left of the 1.
- I want to put them in order.
- I have a 2, another 2.
- Let me stack that above my first 2.
- I have another 1.
- Let me stack that above my other two 1's.
- I have another 0.
- Let me stack it there.
- I have another 1.
- Then I have another 2.
- Another 1.
- I have two more 0's.
- 0, 0.
- I have two more 2's.
- I have a 3.
- I have two more 1's.
- Another 3.
- And then I have a 6.
- So no 5's, and then I have a 6.
- And that space right there was unnecessary.
- But right here I've listed-- I've just rewritten those
- 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.
- So I have one, two, three, four 0's.
- I have one, two, three, four, five, six, seven 1's.
- I have one, two, three, four, five 2's.
- I have one, two 3's.
- I have one 4, and one 6.
- So we could write it this way.
- We could write the number, and then we
- can have the frequency.
- 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.
- 1 showed up seven times in this data set.
- 2 showed up five times, 3 showed up to two times, 4
- showed up one time, 5 didn't show up, and 6
- showed up one time.
- All I did is I counted this data set, and I did this
- first. But you could say how many times do I see a 0?
- I see it one, two, three, four times.
- How many times do I see a 1?
- One, two, three, four, five, six, seven times.
- That's what we mean by frequency.
- Now a histogram is really just a plot, 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 the exact number doesn't
- repeat, oftentimes people will put the numbers
- into buckets or ranges.
- But here they fit into nice little buckets.
- You have the numbers 0, 1, 2, 3, 4, 5, and 6.
- This is the actual numbers.
- And then on the vertical axis we're
- going to plot the frequency.
- So one, two, three, four, five, six, seven.
- So that's 7, 6, 5, 4, 3, 2, 1.
- So 0 shows up four times.
- So we'll draw a little bar graph here.
- 0 shows up four times.
- Draw it just like that.
- 0 shows up four times.
- That is that information right there.
- 1 shows up seven times.
- So I'll do a little bar graph.
- 1 shows up seven times.
- Just like that.
- I want to make it a little bit straighter than that-- 1 shows
- up seven times.
- 2-- I'll do it in a different color-- 2 shows up five times.
- Do a bar graph, go all the way up to five.
- 2 shows up five times.
- 3 shows up two times.
- We have one 3, two 3's.
- 4 shows up one time here.
- 5 doesn't show up at all.
- So it doesn't even get any height there.
- And then finally, 6 shows up one time.
- So I'll do 6 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.

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