 Hello, we are now going to discuss types of graphs. So there are several different types of graphs that can be used to visually represent data. This includes but is not limited to dot plots, stem plots, or stem and leaf plots as you may know them as, pie charts or circle graphs, line graphs, time series graphs, bar graphs, and Pareto charts. First let's start with the dot plot. It's literally a number not number line where dots are placed above the number line to represent frequencies of data values. So for instance, below the number line you have your data values. Each time it occurs, you put a dot above that data value. So as you can see we have 15 dots to represent the 15 students. So data was collected for the number of blue M&Ms in a standard bag. Let's create a dot plot for the given data for the number of blue M&Ms in a bag. So perhaps the most exciting thing for me about this question is blue M&Ms are actually included in bags of M&Ms during my lifetime. I was actually part of the poll where we got to vote on what color would be next. So that's why this question is awesome. So I have my number line. We need to list my data values. I go as low as 6. I go as high as 15. So I'm literally going to label my number line from 6 to 15. So go through each data value. You see that I have an 8. That means you put one dot or put a mark above 8. You have a 10. You have a 15. So a dot above 10 or dot above 15. You have a 9 and a 7, a dot above 9, a dot above 7. You have a 6 and a 7. That's a dot above 6, another dot above 7. You have an 8 with two 9s. So a dot above 8, two more dots above 9. You have three 8s in a row, tick, tack, toes. So add another three dots above 8. And then you have a 10. So put another dot above 10. So looking at this, you can tell that the highest frequency was 8. And then there was one unusual bag that had 15 blue M&Ms in it. But this is a nice way to visually represent the data. It allows us to see what's going on rather than looking at a bunch of numbers. A stem plot or stem and leaf plot represents data by separating each data value into two parts. You have a stem, which is usually your higher place value or your leftmost digit of a number. And then you have your leaf, which is your smaller place value. So the stem is usually your higher place value. And then your leaf is typically a lower place value. So in this case, I have a stem of 2 and a leaf of 0. This means 20. A stem of 2, a leaf of 3. This is read as 23 and so forth. You have a 5 as a stem and a 2 as a leaf. This is 52. You have a 5 as a stem and 5 as a leaf. This is 55. Oftentimes, you'll see a key at the bottom of your stem and leaf plots. And you'll see 5, line 2, or something like that. And that means 52. That'll tell you how to read the stem and leaf plot. So sometimes you see a key that tells you that the 5 represents a 10's place and the 2 represents a 1's place. Pie charts. It uses wedges in a circle to represent categories. The wedges are proportional in size to the percent of individuals or items in each category. The wedges do make up 100% of the data. So my entire circle represents 100%. So use the pie chart of hours Alex spent on activities one Saturday to answer the questions. What percent of the day did Alex spend studying? So we have 24 hours total in my pie chart. Tell me hours are in a day. That's what my numbers should add up to. What percent of the day did Alex spend studying? So to do this, all I have to do is find the studying hours and divide by the total hours. And then I'll convert to a percentage. So how many hours out of 24 did Alex spend studying? It appears that he spent four. Four out of 24. We'll divide those two numbers using your calculator and you get 0.17. So as a percentage, you move the decimal to the right two spots or you multiply by 100. That's 17% of Alex's Saturday was spent studying. Yikes. Well, studying is important, but to me, what's more important would be eating and sleeping. Who has time for that sometimes, right? Well, what percent of the day did Alex spend eating and sleeping? Well, out of 24 hours, how many hours did Alex spend eating and sleeping? Well, eating was two. Sleeping was seven. Not that, Alex. Not that. That's nine out of 24. Divide. When you divide those two, nine over 24 is actually going to give you. It'll actually give you 0.375, which remember to turn this into a percentage. Move the decimal to the right two spots and you get 37.5%. That is how long or what percent of the day Alex spent eating and sleeping. A line graph is a graph where the x-axis consists of data values and the y-axis consists of frequencies. So you have data values on the x-axis, frequencies on the y-axis. Frequency points are connected using line segments. In a time series graph, it displays data that has been collected at specific points in time. So literally for time series, my x-axis represents time. So time is my x-axis. All right, so for instance, you could look at plant height over 10 days. You have days one all the way through 10. And you can see the height of the plant gradually increasing. So that's the cool part about these sorts of graphs. They show these trends in data over time. So obviously, the plant's growing. We can see that. We can find out where the biggest growth occurred between what two days, where's the sharpest line. So that's just an example of line graphs and time series graphs. Data was collected for the number of customers who shopped at a newly opened store for the first 10 days. Create a time series graph. What is the trend? So this is going to be number of customers. That's what our little graph's going to display. So I'm going to draw my y-axis. And I'm going to draw my x-axis. So I have 10 days that I have to put on here. So day one through day 10. So 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Then if you look at my customer counts, it looks like I go as low as 195, and I go as high as, well, 325. So I'm going to use a scaling of 50. So 50, 100, 150, 200, 250, 300, and 350 is where I can stop. Because 325 is my highest value. And then we draw our dots. So on day one, we had 325. Let me be a little bit proper here. Day is my x-axis, and then frequency is my y-axis. I would write this vertically, but I don't feel like tilting my head sideways right now. All right, day two, you got 313. Day three, you have 291, so just below 300. Day four, you got 275. Not drawn to scale, by the way. Day five, you have 250. Day six, you also have 250. Day seven, 230. Day seven, 230. Day eight, you got 205. Day nine, 197, so just below 200. And day 10, you got 195. It's about the same as day nine, very close anyway. Then we'll connect our dots. Try and make the lines as straight as possible. Butchines can make inferences about this data based on the trend that you see. Like I said, graphs visually represent our data. And if you can notice, obviously what's happening is the customer count is decreasing based on the day. Over time, the trend is decreasing. So what is the trend? Number of customers is decreasing. And why would that be? We have to try and come up with explanations or hypotheses about why this could be. Well, I would say if this is a new store, obviously people are hyped up about a new store and they run special sales when they open. And then over time, the customer count or number of people coming in will level out. So to speak, this was actually the case for one of the grocery stores I worked for when we did our grand reopening. High customer count at first and it kind of trickled back back to normal. Now bar graphs, we're not gonna really make any, but a bar graph literally shows categories and each of the bars represents frequency of each of the categories or each of the things. So like total passenger complaints. You have number of complaints on your Y-axis. You have your airlines on your X-axis. And here you can tell, okay, United has the most complaints, then American, Delta and so forth. But you do need to be aware. Don't just look at graphs without thinking about them. Who do you think of these airlines has more customers? Probably United has more customers than Alaska. Probably United has more customers than Pinnacle. So keep that in mind. Don't just say, oh, United is just terrible or Americans just terrible. Think about how many customers they serve. Obviously more customers, there might be more complaints. A Pareto chart just consists of bars that are ordered by category size. So don't be scared about the word Pareto. Literally the categories or the bars are put from largest to smallest. So United comes first, American, Delta, Alaska, Pinnacle and Airtrain. So all it is is a bar graph where the bars are in greatest to least order. And I also want to just give you a little bit of a fair warning here about graphs that deceive. So graphs can be misleading or one or more, one or both of the axes begin at non-zero values so that differences are exaggerated. So for instance, on my graph on the left, I have weekly grocery store sales. I start my scaling on the y-axis at zero and then I increment by 50,000 all the way till I get to 400,000. So if I look, store A, store B, store C, it looks like they relatively have the same sales. They're pretty close to one another. They're within $50,000 of each other. That's the range. But if you look at the graph on the right, weekly grocery store sales, I see that they start my y-axis at $270,000 and they use a scale of $10,000 till they get to 360. Now look at how this changes things. You see store A, the store B, it looks like there's a huge difference between them when it's only $50,000 in sales. So here they use this graph to make it look like store A is performing terribly while store B is excelling and doing awesome when it's only a $50,000 difference. So please watch your scales on your bar graphs. Dealerships can do this with gas mileage. They compare gas mileage on cars across different makes and models. So be very careful, look at your scale. Don't just look at something and believe it. So that's all I have for you for now. Hope you enjoyed. Thanks for watching.