1 00:00:00,090 --> 00:00:05,760 We've said over and over throughout this section that our goal with any chart or graph is just to display 2 00:00:05,760 --> 00:00:10,080 the data or conclusions that we're trying to communicate as clearly as possible. 3 00:00:10,110 --> 00:00:16,620 Part of what that means is, of course, being aware of some common plot pitfalls, like, for example, 4 00:00:16,650 --> 00:00:21,970 a misleading vertical axis, which is something that unfortunately is too common. 5 00:00:21,990 --> 00:00:29,040 In this chart here, we clearly have a bar graph and at first glance it looks like there's a huge increase 6 00:00:29,040 --> 00:00:31,710 between 2022 and 2023. 7 00:00:31,710 --> 00:00:36,120 And so we might expect some dramatic change between these two years. 8 00:00:36,120 --> 00:00:44,430 But when we look at the Y axis, what we see is that the y axis not only starts at 34%, but tops out 9 00:00:44,430 --> 00:00:46,290 up here at 42%. 10 00:00:46,290 --> 00:00:52,020 So the difference between these two years is actually not that significant at all. 11 00:00:52,020 --> 00:00:56,340 In 2022, it looks like we're sitting at about 35% maybe. 12 00:00:56,460 --> 00:01:00,150 And in 2023, it looks like we're sitting at about maybe 40%. 13 00:01:00,150 --> 00:01:05,850 So an increase from 35% to 40% is really not that significant at all. 14 00:01:05,880 --> 00:01:14,010 Imagine instead, if we started this y axis at zero and it went all the way to 100, the bars representing 15 00:01:14,010 --> 00:01:20,130 these two years would look almost identical, and we certainly wouldn't interpret the bar chart as if 16 00:01:20,130 --> 00:01:27,390 there was a big change between 2022 and 2023, but sketched out this way with this particular y axis, 17 00:01:27,390 --> 00:01:29,730 it looks like the increase is dramatic. 18 00:01:29,730 --> 00:01:33,960 So we have to be really careful about the scale of this vertical axis. 19 00:01:33,960 --> 00:01:38,790 In this case, the scale is probably too small, but we can also have the opposite scenario where the 20 00:01:38,790 --> 00:01:40,320 scale is too big. 21 00:01:40,320 --> 00:01:45,660 And so a change between bars is actually dramatic, but it doesn't appear dramatic because the scale 22 00:01:45,660 --> 00:01:47,460 of the vertical axis is too big. 23 00:01:47,460 --> 00:01:52,080 So we have to be aware of the scale of any axis in any chart. 24 00:01:52,080 --> 00:01:57,060 We also need to think about where it makes sense to start and end the axis like we talked about here 25 00:01:57,060 --> 00:02:01,800 in this particular chart, when we're talking about percentages, it probably makes more sense to start 26 00:02:01,800 --> 00:02:07,440 the vertical axis at zero and ended at 100 instead of starting it at 34 and ending it at 42. 27 00:02:07,440 --> 00:02:13,140 In fact, it's usually a best practice to start the vertical axis at zero unless we have really good 28 00:02:13,140 --> 00:02:14,850 reason for not doing so. 29 00:02:14,850 --> 00:02:19,860 If we think the data is actually more clear, if we don't start at zero, maybe we have negative values 30 00:02:19,860 --> 00:02:23,010 in our data and we need to start at some negative value. 31 00:02:23,010 --> 00:02:26,760 So we just need to be really careful about the start and end points, the scale. 32 00:02:26,760 --> 00:02:30,420 We also need to think about a consistent scale across the axis. 33 00:02:30,420 --> 00:02:37,440 So for instance, with this chart here, if we look at the horizontal axis, we have years across the 34 00:02:37,440 --> 00:02:38,310 horizontal axis. 35 00:02:38,310 --> 00:02:44,850 So this is 1960, 1970, 1980, and then all of a sudden we jump to the year 2000 and then the year 36 00:02:44,850 --> 00:02:48,840 2020, which makes this horizontal axis really confusing. 37 00:02:48,840 --> 00:02:51,030 It feels compressed over here on the left side. 38 00:02:51,030 --> 00:02:53,850 And then like there's bigger jumps over here on the right side. 39 00:02:53,850 --> 00:02:59,430 It's hard for us to envision where we are in time as we move along this horizontal axis because we don't 40 00:02:59,430 --> 00:03:01,170 keep the scale consistent. 41 00:03:01,170 --> 00:03:05,880 We also have a problem here where the horizontal axis isn't labeled very well. 42 00:03:05,880 --> 00:03:10,950 Yes, we say here that the horizontal axis represents year, but because we're crossing over from the 43 00:03:10,950 --> 00:03:18,150 1900s to the two thousandths to start at just 60, 70, 80, and then suddenly show just zero zero and 44 00:03:18,150 --> 00:03:22,050 then 20, it just makes this axis more difficult to interpret. 45 00:03:22,050 --> 00:03:26,940 So whenever we're building a chart or a graph, not only do we want to be correct, we don't want to 46 00:03:26,940 --> 00:03:31,800 have data that's wrong in our graph or in our chart, or we don't want the chart to be misleading, 47 00:03:31,800 --> 00:03:34,920 but we also want to do everything we can to make it clear. 48 00:03:34,920 --> 00:03:39,960 So even if there was nothing wrong about this horizontal axis right, we could fill it in here with 49 00:03:39,960 --> 00:03:42,510 90 and then ten. 50 00:03:42,510 --> 00:03:45,780 Even doing that would help make things a little more clear. 51 00:03:45,780 --> 00:03:51,930 It also might make things more clear to say here 1960 and then show the year 2000. 52 00:03:51,930 --> 00:03:56,130 Just making those couple of changes makes it a lot easier to read the horizontal axis. 53 00:03:56,130 --> 00:04:02,220 So we want to do everything we can to first, of course, not be wrong, but then second, be as clear 54 00:04:02,220 --> 00:04:04,620 as possible with how we're displaying information. 55 00:04:04,620 --> 00:04:10,620 So this axis wasn't labeled really well in this chart over here, nothing's labeled well at all. 56 00:04:10,620 --> 00:04:12,450 We don't have a chart title. 57 00:04:12,450 --> 00:04:15,180 We don't even know what's being shown here in the chart. 58 00:04:15,180 --> 00:04:19,769 And we probably be helped if we maybe displayed the percentage at the top of each bar. 59 00:04:19,769 --> 00:04:24,480 Something like this, maybe 35.5%, let's say. 60 00:04:24,480 --> 00:04:28,260 And then up here, let's say 40.2%. 61 00:04:28,260 --> 00:04:33,600 If those are the real values, because of the scale of this vertical axis, it's maybe a little hard 62 00:04:33,600 --> 00:04:35,400 to tell the exact value of these bars. 63 00:04:35,400 --> 00:04:40,020 Just adding these values here brings extra clarity to this particular chart. 64 00:04:40,020 --> 00:04:45,510 We should probably also have here a title like we said, so we know what the chart is displaying. 65 00:04:45,510 --> 00:04:48,810 We just want to make sure everything's labeled as well as it can be. 66 00:04:48,810 --> 00:04:53,940 This line plot over here on the right is another example of a chart that's misleading. 67 00:04:53,940 --> 00:04:59,840 The title of the graph said that college is no longer worth it and tries to show that based on. 68 00:04:59,940 --> 00:05:06,240 On the discrepancy between the rising cost of tuition and the relatively stable earnings that can be 69 00:05:06,240 --> 00:05:09,740 expected after a person completes college and earns their degree. 70 00:05:09,750 --> 00:05:15,030 The problem is not only am I giving you extra information there because the legend here only says earnings, 71 00:05:15,030 --> 00:05:18,780 it doesn't say annual earnings or specify some other period. 72 00:05:18,780 --> 00:05:25,650 But in addition to that problem, what the chart is actually showing is total cost of tuition over the 73 00:05:25,650 --> 00:05:28,140 course of the entire college program. 74 00:05:28,140 --> 00:05:30,270 So let's say that's over four years. 75 00:05:30,270 --> 00:05:34,520 The mean total cost has risen to close to $95,000. 76 00:05:34,650 --> 00:05:42,390 The graph is comparing that value to mean earnings of that graduate, but on an annual basis. 77 00:05:42,390 --> 00:05:48,360 So it's showing that the graduate can expect to earn about $50,000 per year after they graduate. 78 00:05:48,360 --> 00:05:53,070 But this line plot makes it look like there's some huge discrepancy in the cost. 79 00:05:53,070 --> 00:05:58,800 But if we really think about the annual earnings of the Graduate, if they earn 50,000 a year, then 80 00:05:58,800 --> 00:06:07,170 in their first five years of employment, they can likely expect to earn at least 250,000, 50,000 a 81 00:06:07,170 --> 00:06:11,580 year times five years, maybe more, if they get a small raise each year. 82 00:06:11,580 --> 00:06:17,190 And that is compared to the total cost of the four year degree of close to. 83 00:06:18,010 --> 00:06:18,970 95,000. 84 00:06:19,630 --> 00:06:24,130 And when we compare those two figures, the cost of college looks a lot more reasonable. 85 00:06:24,130 --> 00:06:30,010 Whereas if we compare them this way, the cost of college looks extremely unreasonable because of the 86 00:06:30,010 --> 00:06:30,490 difference. 87 00:06:30,490 --> 00:06:37,060 The discrepancy between this high cost of tuition and the apparent low earning potential of the graduate. 88 00:06:37,060 --> 00:06:41,770 We'll also sometimes see in the real world charts like these ones. 89 00:06:41,770 --> 00:06:43,450 This is a pie chart. 90 00:06:43,450 --> 00:06:47,860 Let's say it's trying to represent support for different political candidates. 91 00:06:47,860 --> 00:06:52,300 First of all, just like this bar chart, we have no title for the chart. 92 00:06:52,300 --> 00:06:59,140 We have no legend, and including both of those would be really helpful if we had a legend here where 93 00:06:59,140 --> 00:07:06,130 we said that Green was supports candidate A and Blue was supports candidate B, etc. that would help 94 00:07:06,130 --> 00:07:08,250 us to interpret this pie chart. 95 00:07:08,260 --> 00:07:10,360 We have another problem here with the pie chart. 96 00:07:10,360 --> 00:07:12,940 The data is just flat out misleading. 97 00:07:12,970 --> 00:07:17,650 A pie chart should always sum to 100% each piece of the pie. 98 00:07:17,650 --> 00:07:20,560 When we add them all up, they should sum to 100%. 99 00:07:20,560 --> 00:07:28,180 And here these percentages are summing to 165%, which makes the chart completely invalid and unreadable 100 00:07:28,180 --> 00:07:28,930 entirely. 101 00:07:28,930 --> 00:07:33,970 So not only is it just flat out wrong, but we don't really understand what it's saying because we have 102 00:07:33,970 --> 00:07:35,680 no title, we have no legend. 103 00:07:35,680 --> 00:07:41,680 And on top of that, pie charts are often not a great way of displaying most data in general, because 104 00:07:41,680 --> 00:07:46,900 they can be hard to read in the sense that it's difficult to compare each slice against the other. 105 00:07:46,900 --> 00:07:53,050 We can tell that this purple section here appears to be the biggest section, but looking at green versus 106 00:07:53,050 --> 00:07:58,660 blue, if we don't have these labels at first glance, it's hard to interpret whether green is bigger 107 00:07:58,660 --> 00:08:01,150 than blue or vice versa, or they're the same size. 108 00:08:01,150 --> 00:08:07,210 So for something like this, a comparative bar chart might be just a better way to display the data 109 00:08:07,210 --> 00:08:07,990 in general. 110 00:08:08,200 --> 00:08:14,830 So the whole idea here is that whenever we're trying to display any kind of information, we've collected 111 00:08:14,830 --> 00:08:21,220 data and now we want to communicate that data in some summarized way to somebody else, we really need 112 00:08:21,220 --> 00:08:25,390 to think about choosing the best. 113 00:08:26,090 --> 00:08:28,040 Chart type, right? 114 00:08:28,040 --> 00:08:30,560 Is a bar chart the best option? 115 00:08:30,560 --> 00:08:32,510 Should we use a line plot instead? 116 00:08:32,510 --> 00:08:34,539 Should we use a box and whisker plot? 117 00:08:34,549 --> 00:08:35,900 What kind of graph? 118 00:08:35,900 --> 00:08:40,100 What kind of chart is the best way to display this information? 119 00:08:40,100 --> 00:08:45,770 Once we've chosen the chart that we think best communicates the data that we have to display, then 120 00:08:45,770 --> 00:08:53,900 we want to think about all of the aspects of the chart that affect the clarity of the information being 121 00:08:53,900 --> 00:08:54,560 displayed. 122 00:08:54,560 --> 00:08:56,270 So we should probably have a title. 123 00:08:56,270 --> 00:08:58,520 We should probably label both axes, right? 124 00:08:58,520 --> 00:09:03,380 We should probably have set up here that this horizontal axis represents a year. 125 00:09:03,380 --> 00:09:07,190 We should label this vertical axis based on whatever it represents. 126 00:09:07,190 --> 00:09:09,590 We should have a legend, if that's appropriate. 127 00:09:09,590 --> 00:09:12,320 Over here, we had a legend for the line plot. 128 00:09:12,320 --> 00:09:14,870 We should maybe give the units for each axis. 129 00:09:14,870 --> 00:09:21,440 So over here we said that this vertical axis is dollars in units of thousands, so we can interpret 130 00:09:21,440 --> 00:09:22,130 this 45. 131 00:09:22,130 --> 00:09:24,950 Here's 45,000 over here. 132 00:09:24,950 --> 00:09:29,450 This vertical axis, we know we have percentages because we see 34% here. 133 00:09:29,450 --> 00:09:33,860 So we know we have percentages, but we don't know what this vertical axis is indicating. 134 00:09:33,860 --> 00:09:37,070 So we want to think about labeling everything that we can. 135 00:09:37,070 --> 00:09:41,600 We want to think about the scale of each axis and the scale of the data that we're displaying. 136 00:09:41,600 --> 00:09:43,490 We don't want the scale to be too small. 137 00:09:43,490 --> 00:09:45,350 We don't want it to be too big. 138 00:09:45,350 --> 00:09:47,660 We want the scales to be consistent. 139 00:09:47,660 --> 00:09:53,240 We want to start our scales at zero, unless some other starting point definitely makes more sense. 140 00:09:53,240 --> 00:09:58,010 And we want to make sure that the point that we're actually communicating is a valid one. 141 00:09:58,010 --> 00:09:59,660 So let's maybe say here. 142 00:10:00,390 --> 00:10:06,900 Validity right in this chart here, we're communicating a significant increase across years when in 143 00:10:06,900 --> 00:10:09,570 fact the increase isn't that significant at all. 144 00:10:09,600 --> 00:10:15,360 Over here, we're communicating a significant difference between tuition across four years and then 145 00:10:15,360 --> 00:10:17,360 earnings for just one year. 146 00:10:17,370 --> 00:10:19,950 Maybe that's really not the most appropriate comparison. 147 00:10:19,950 --> 00:10:25,560 Maybe we should compare cost of tuition to expected lifetime earnings or earnings over the first five 148 00:10:25,560 --> 00:10:26,820 years or ten years. 149 00:10:26,820 --> 00:10:32,100 In other words, we really might not be communicating the best conclusion based on the way that we're 150 00:10:32,100 --> 00:10:35,370 displaying our data or what we're including in our data at all. 151 00:10:35,370 --> 00:10:40,980 And then the last thing probably is just pure accuracy or correctness. 152 00:10:40,980 --> 00:10:43,410 This pie chart here is just wrong. 153 00:10:43,440 --> 00:10:48,420 A pie chart always has to sum to 100% by definition, and this one doesn't. 154 00:10:48,420 --> 00:10:50,910 If the data were displaying is just incorrect. 155 00:10:50,910 --> 00:10:52,560 We obviously want to fix that. 156 00:10:52,560 --> 00:10:56,910 Maybe this 35.5% here was actually wrong in this bar. 157 00:10:56,910 --> 00:11:00,420 Should have been all the way up here at 45%. 158 00:11:00,420 --> 00:11:07,080 And after we build out our bar chart, we realize that and we can correct the bar and label it appropriately. 159 00:11:07,080 --> 00:11:13,110 Maybe we had a mistake here where in our line plot, instead of having 85 right here, maybe we actually 160 00:11:13,110 --> 00:11:13,950 had 90. 161 00:11:13,950 --> 00:11:17,130 And that's just a mistake and we need to change it to 85. 162 00:11:17,130 --> 00:11:21,930 So these are all things that we want to think about, starting primarily with just choosing the best 163 00:11:21,930 --> 00:11:22,380 chart. 164 00:11:22,380 --> 00:11:27,000 Working through each of these questions is my chart clear? 165 00:11:27,000 --> 00:11:30,090 Is the point I'm trying to make even valid? 166 00:11:30,120 --> 00:11:32,040 Is everything in the chart accurate? 167 00:11:32,040 --> 00:11:37,890 And if we've done all that and we've built a chart or a graph that we feel accurately communicates the 168 00:11:37,890 --> 00:11:43,500 data we've collected and shows the point that we're trying to make by summarizing the data in the chart 169 00:11:43,500 --> 00:11:49,380 or the graph, then we can feel pretty confident that we've created a good chart or a graph or a plot 170 00:11:49,380 --> 00:11:55,020 that's actually doing a good job displaying the conclusion that the data should reveal.