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## Types of DI Graphics

Now we can talk about different types of graphics. The GRE Data Interpretation can present information in the form of several different kinds of graphs or charts. In this video, we will discuss various categories of charts. Perhaps the easiest kind of chart is a pie chart. This is quite likely already very familiar.

You probably have seen pie charts most of your life. Typically the data interpretation doesn’t present questions that depend only on a single pie chart. That would be a bit too easy. Instead the pie charts are usually paired with another type of chart and one breaks down a region of the other.

So for example a slice of the pie chart might be subdivided in a bar chart. Or a bar graph. One particular bar in a bar graph might be subdivided into a pie chart. So pie charts usually appear paired with some other kind of graph like that. Another common graph is a line chart, and the line may connect dots on a particular graph.

It could be connections by straight line segments like this, or it could be a smooth curve collecting them, connecting them. Either one is a line chart. It’s basically the same information. It’s kind of stylistic difference. It could appear in either form.

And almost always, the horizontal axis is time. This is called a time plot because it demonstrates a trend over time. Notice that this particular graph is a very happy story. What we have here is US unemployment dropping more or less continuously throughout 2014. And that’s very good news, that’s precisely why the United States economy got much stronger through the year 2014.

US unemployment is a leading economic indicator in the United States economy. And to have US unemployment drop, especially to drop pre, precipitously, or continuously over the course of a year, that is exceptionally good news for the economy. Now, we will talk about bar graphs. The bars may be vertical or horizontal.

I want to make very clear, there is no meaningful mathematical difference between horizontal bars and vertical bars. It’s purely a stylistic difference. In other words it’s an artistic thing, which one would look better, there’s no meaningful mathematical difference. The bars can be vertical or horizontal.

Doesn’t matter. The bars may represent the different members of a category or different intervals of time. The big idea is that the scale is parallel to the bar, and this indicates the variable in question and the length of the bar indicates the amount of contribution of that element.

So the length of the bar is what is really important. That’s where the data is displayed in a bar graph. So here’s a bar graph with horizontal bars. Notice just from an artistic perspective, if we made these vertical bars, well at the bottom we have some long names there. Banna, cantaloupe, grapes (a cup).

That would space out the bars, and just artistically, or, or design-wise, it would be kind of a mess, whereas it’s much neater to design this in terms of horizontal bars. Again, that’s a design choice. It has no mathematical consequences. Notice that the scale, calories, is also horizontal, and that the length of each bar gives us the calories in that piece of fruit.

So for example, probably not surprising, bananas are high in calories. But also apples and pears are very high. That’s a little surprising. Whereas cantaloupe and kiwi, those are very low in calorie, compared to other fruits. Here’s a graph with vertical bars.

Here, the scale is also vertical, and indicates the number of sales for each day of the week. So this is a, a company, looks like on average the highest sales are on Wednesday, Wednesday and Thursday are good days. Friday is really the lowest day, it’s kind of a drop off day. In a segmented bar graph, each bar consists of two or more segments denoted by different colors or patterns.

The segments break down the overall variable into relevant parts. So for example, here we have two different divisions of a company. And so, notice that we might be interested in just the sales of division one. Division one has it’s highest sales on Wednesday. We might be interested in just the sales of division two. Division two, well it looks like Monday and Thursday are pretty close for division two.

Tuesday is, is clearly the, the, the lowest sale day for division two. But we might also be interested in the overall pattern. And it turns out, because the overall company would have the total sales of division one plus division two. This is precisely when you use the segmented bar chart. If you’d be interested in either the number represented by the length of each individual segment, or you might be interested in the sum.

And here the sum would be the total sales of the whole company. The whole company’s best sale day is on Wednesday, clearly. And it’s slowest sales day is on Friday, even though division two has better sales on Friday. By contrast, a side-by-side bar graph, each category has not one bar, but two right next to each other.

The two bars typically represent two different agents, and this format allows for direct comparison. So here, we have Company 1, Company 2. Here we don’t care about adding the sales because it’s two different companies. The people at Company 1 care about sales at their company, the people at Company 2 care about the sales of their company.

No one cares about the sum of those sales, so that’s why it doesn’t make sense to do a segment of our graph here, we’re just doing a side by side bar graph. So notice Company 1 has it’s best sales on Wednesday, Company 2 seems to be following a different pattern, it’s peaking on Monday and Thursday. And, in fact, at the ends of the week when Company 1 has low sales, Company 2 outsells Company 1 on both Monday and Friday.

So very interesting patterns here. Here’s a practice question with a time graph. Pause the video, work on this and then we’ll talk about this. Okay. So the yearly cost in revenue for FabCo Corporation is shown. So it looks like the costs, the purple line, that stays more or less flat along the bottom where the revenues seem to be fluctuating wildly.

They’re kind of going up. There was a big drop in 2008. Presumably because of the subprime mortgage crisis in 2008. And then after that it rose steadily. So, very interesting pattern and then we’re told that profit equals revenue minus cost.

So that’s something that you may have to know. Certainly if you were taking a test like the GMAT you would have to know that profit equals revenue minus cost. But here the question was nice enough to tell you that. What that means is that revenue is the top graph, cost is the bottom graph. So profit is the distance between the top graph and the bottom graph.

So we can see, looks like the profit is growing, growing, it shrinks to something really small in 2008. Although, there still was a small profit in 2008. And then the profit starts to grow steadily, from that point. After 2004, so we’re not considering before 2004, in this region, the highest percent from the previous year, is what year?

Well, let’s see. 2006. That’s a little increase from year to year. That’s not much of a percent. 2008. Well 2008 was actually a drop from the previous year, so it’s definitely not 2008.

But 2009. Look at this. Here we had a profit of less than a million. Here we went up to about two million. So that is more than 100% increase. So that is a huge increase in profits.

From one million to two million. From 2009 to 2010, well we go from two million to something slightly less than four million. So almost 100%, but not quite 100%. So it turns out that the biggest percent profit, again, this is not, remember the difference between numerical increase and percent increase, we had a bigger numerical increase in going from 2009 to 2010, that was a huge numerical increase.

But not as big a percent increase and here we’re asked about the percent. So c is the best answer here. Another type of bar chart is the histogram. Technically, hyper-technically, histograms are not really bar charts. Yes, they have bars on them, but they’re actually. If you took a, a formal statistics class, you’d see that histograms are actually considered a different category from bar charts.

We’ve already talked about these in the normal distribution video in the statistics module. And as I’ve said, although technically, histograms have bars, they are not bar graphs because the bar represents regions of a numerical variable, not different discreet categorical variables. The heights of the bar in the histogram indicate the frequency of values.

That is the number of occurrences of the values that fall in a given range. Here’s a typical histogram. So presume we polled a number of high school students, and we ask them how many hours a week do you watch, did you watch TV last week. And then we got their numerical answers, and we grouped them in a hist, histogram. So notice that most of the respondents, 35 of the respondents, the largest number of respondents, responded in the six through ten range.

So they, they named a number somewhere between six and ten. The next highest was 11 through 15. And then there were some outliers, some very high outliers. People saying that they watched 25 or 30 or 35 hours of television in the week. So. There were few respondents who gave numbers that high.

And notice again the categories are not different discrete variables, they’re ranges of a quantitative variable. Numbers of hours of TV wa, lost, law, watched last week, we’re just looking at subdivisions of that particular variable. So here’s a practice question.

Pause the video, and then we’ll talk about this. Okay. In a survey 86, very important, 86 students were asked about their TV watching habits. Half of 86 is 43.

And so what that means, if we divide the list in half, there’s 43 below the median and 43 above the median. So between the 43rd and the 44th person, that’s where the median would be. Well let’s think about this. There are, looks like 13 people in this category. And then there are 35 people in that category.

So 13 plus 35 is 48. And so it means that by the time we get to ten, we were at the 48th person. We’ve already passed this region that, where, between the 43rd and the 44th person, so the median has to be in this particular column here. It has to be in the six through ten range, the only number here in the six through ten range is B, seven.

One final category of charts is scatter plots, and that’s kind of a complicated topic. So, they’ll get their own lesson in the next video.

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