Okay, so now we'll talk about visualization of data. Now, it's one thing to have data and do some analysis on it, have descriptive statistics as we saw before. It's another thing to actually get a sense of what the data looks like. And often, this is very useful because visualizing the data could lead to some insight that is otherwise not possible or easy to access. So let's look at some examples. Here's one example. This is the data gathered by The New York Times, and it's looking at the renting and buying trends. So now there's underlying data about home prices, about rental prices. And you can look at those data, but it may not give you enough information, or it may not give you easily accessible information. What you really want to do is to make a decision whether you should buy a home or rent it. And so what this is is actually interactive graphics, but even if you forget that, what you see here is the home prices trend using a bar chart, so this is a bar chart, and some information about rental prices. So you could immediately see the meaningful data presented to you visually. And that helps us in making a decision, or at least exploring some avenues that otherwise may not be clear just by looking at the data. All right, so having the right kind of visualization could help us discover new phenomena, make better sense out of the data, and communicate information in a better way. So we'll just see some examples of how visualization could be helpful in creating insights or deriving decision-making insights. Okay, so, here's one example. It's an example of a histogram. With a histogram, what typically happens is we are representing a distribution. So in this case, it's a distribution of people working. And so on the x-axis, we have the time of day during the weekday, and on the y-axis we have percentage of people working. So that's the population we're trying to portray here. Now, you can see there are all kinds of curves here. There are two that are highlighted. One is for all jobs, which is this orange-red kind of line, and the other one is construction and mining workers, which is this blue curve. And of course, these curves are coming from some underlying data. But by just looking at this visualization, we can derive some insights easily. All right, so for instance, the construction and mining workers, more of them tend to start working before other jobs. So they kind of start early, and they're also finishing early. So as you can see, toward the end of the day, they're finishing before, on average, other jobs, right? You can also see that there is a dip here for not just construction mining workers, but pretty much all the other jobs. And perhaps, that's the lunch hour that fewer people are working. I mean, there's still a good number of people working, but it drops from that 80% to about 50%. And then of course, there are all these other lines that represent different jobs. So if you're interested in any of those jobs, then you can highlight that and you can analyze that. But you see how just looking at this, we are able to do the kind of analysis that doesn't require running numbers and doing other things. Of course, this is a rough sense, but it can be just enough to at least form a hypothesis that, if interested, then can be further tested. But just looking at this data could be a very, very powerful thing. Here is another example. This is an example of a bar chart. Now, before we saw a bar chart that was with vertical bars. This is with horizontal. And so a bar chart comes in all kinds of flavors. What we see here are five bars. They represent five boroughs of New York City, and what they're showing is the trees on the streets and the variety of those trees. So not only do these bars represent the total number of trees in those five boroughs, but also within each bar, you see there's different segments in different colors, which represent different kinds of trees. So again, immediately, just looking at this, you're able to compare different boroughs, but also their distribution of trees. Now, this is not giving you very detailed, precise information, but just looking at this, it could be very helpful to even see what you want to do with it next, what kind of question you want to ask. Maybe you have a hypothesis that you can test. So this is a good example of a bar chart visualization. Now let's look at something that's closer to social media. Here's what's called time plot. This is done using the tweets during the State of the Union address by the president of the United States. Now, the State of the Union Address starts at around 9 o'clock and it goes on for about an hour and a half. And during that time, all these tweets are happening from different parts of the country, in the US. And so you can see there is the energy hashtag here. There's jobs, fairness, health care, defense. So at different times, there are different hashtags that are kind of prominent and that are related to the actual State of the Union address. So this is kind of a nice way to visualize the trends that are happening across time, but also across geographic regions. And this is quite common in social media data analysis, where the data is very much ephemeral, which means it comes and goes very quickly. And we want to be able to study in a given time, given geographic location, or other parameters. And so it could be happening in real time, or we could look back and do this in a reflective manner. So this is a nice time and space visualization. Okay, so the thing that we discuss here is that data analytics and visualization go hand-in-hand. We can often start with just plotting the data in some way, having some visualization. And that gives us an idea of what kind of analysis we should be doing before we get too deep into it. Visualization can also help us confirm certain beliefs or come up with hypotheses. And the right kind of visualization could be very powerful in conveying a meaning and helping us understand some phenomena or discover some phenomena that may otherwise not be so apparent. And in this video, we discussed histogram, bar chart, and time series visualization. There are several others, of course. Some of the most common ones are line chart, pie chart, box plot, scatter plot. Now, we didn't see how any of these things are generated. But in the following units, when we actually start working with real data, and accessing the data, and doing some analysis, we'll see how some of these things could be generated that will help us with doing our analysis.