In Exercises 11 and 12 construct the Pareto chart.

Question

Box Office Boffo Recent annual gross revenue (millions of dollars) for the leading movie studios are as follows: 20th Century Fox (1082), Buena Vista (3092), Paramount (757), Sony/Columbia (1304), Universal (1772), Warner Brothers (1941). Are these data likely to be reasonably accurate?

Accepted Answer

Hi, everyone. Let's take a look at this practice problem. This problem says recent annual revenue in millions of dollars for the leading music record labels is as follows. Label A, 5300, label B, 8900, label C, 5800, label D, 2500, label E, 3100, and label F, 4200. Construct a Pareto chart to visualize the distribution of revenue. Are these data likely to be reasonably accurate? And below the problem we're given a blank chart on which to create our graph. Now, the first thing we need to do. In order to create a beer chart, is to organize our data starting from the highest revenue going to the lowest revenue. So, we're going to create a new table. The first column is going to be our record label, so that will be labeled as our first column. The next column is going to be the revenue of that live. The 3rd column. is going to be the cumulative revenue, since we'll need that information in order to create our chart. And then the final column. is going to be the percent. Of cumulative revenue. Since we'll need to add that as part of our graph. So we went to List our labels starting from the largest revenue going to the smallest revenue. And if we look at our data, we see that the largest revenue is label B. So, our first row is going to be for label B. It's going to have a revenue of 8900, and the cumulative revenue at this point is just going to be the revenue of label B, which is going to be 8900, and we'll come back and calculate the percent cumulative revenue later on. Now, the label that has the next largest revenue is going to be label C, and it has a revenue of 5800. And that means that the cumulative revenue, when we add the 5800 to the cumulative revenue, we will have 14,000. 700 as our cumulative revenue. The next label that has the next highest revenue is going to be label A. And it has a revenue of 5300. And that brings our cumulative revenue up to 20,000. The next label with the next highest revenue is going to be label F. And it has a revenue of 4200. That brings our cumulative revenue up to 24,200. The next label that we want to look at, it's going to be label E. It has a revenue of 3100, that brings our cumulative revenue up to 27,300. And then our final label that we're going to look at is going to be label D. It has a revenue of 2500. And that brings our total cumulative revenue up to 29,800. So now that we have the maximum cumulative revenue, we can now calculate the percent of the cumulative revenue. So for each label, we're going to take the cumulative revenue and divide it by the total cumulative revenue of the 29,800 and multiply by 100% to get a percentage. So, for label B, we will have the cumulative revenue of 8900. Divided by 29,800. And then that quantity gets multiplied by 100%. And this is going to be approximately equal to 29.9%. The next label we'll look at is going to be label C. It had a cumulative revenue at this point of 14,700. That is going to be divided by the 29,800. And that quantity is multiplied by 100%. And this here is going to be approximately equal to. 49.3%. So for our next label, label 8, it had a cumulative revenue at this point of 20,000. That gets divided by 29,800. that quantity is multiplied by 100%. Which is approximately equal to. 67.1%. For the next record label, label F, the cumulative revenue at this point is 24,200, that is divided by the 29,800. And again, that quantity is multiplied by 100%. And this is approximately equal to. 81.2%. Now, for label E, which is our next one, we had a cumulative revenue of 27,300, that gets divided by the 29,000. 800 And we'll multiply that quantity by 100%. And this is approximately equal to. 91.6%. And then for our final label, label D. The cumulative revenue has reached its max of 29,800. I'll divide that by 29,800. That gets multiplied by 100%. And this is going to be equal to 100%. So now we have all the information that we need to create our chart. So, the first thing we're going to do is put the revenue for each label onto our chart. And so, the first one that we're going to do is label B. It had a revenue of 8900. So, we'll draw a box on our chart that has a height of 8900. On our graph. Using the axes on the left, and we'll label that box as label B. The next highest revenue was for label C. And it had a revenue of 5800, and so we'll draw a box that has a maximum value. Of 5800, and we'll label that box as D. The next The label that we want to look at is label A. It had a revenue of 5300. They will want to draw a box. That has a maximum value of 5300, and we'll label that box as sorry as label A. The next label that we want to look at is label F. It had a revenue of 4200. And so we'll draw a box. That has a maximum value of 4200, and we'll label that with an F, to indicate label F. The next label that we need to draw is label E. It had a revenue of 3100, we'll draw. A box that has a height of 3100. And we'll label that box with an E. And then the final. The label that we need to look at, it's label D. It had a revenue of 2500, and so we'll draw a final box. On our graph, Here, with a height of 2500, and we'll label this as D. So now we just need to draw our cumulative revenue line. And so, starting with box B, On the left Our cumulative revenue was 29.9%. We'll place that point on the graph. Or Label C, the cumulative revenue at this point, was 29.3%, we'll place a point on that autograph with um label C. And then the next point was for label A, with 67.1%, we'll place a point on label A. With a percentage of 67.1%. Next label that we need to look at is F. It had a cumulative, um, a cumulative revenue percentage of 81.2%, we place at that point. On the graph. For label E, it had a percent cumulative revenue of 91.6%. We'll place that point on the graph, and then for label D, it had A percentage, a cumulative revenue of 100%. So now that we All we need to do is to connect these points with a line. Or our percent. Cumulative revenue line. And once we connect all these points, We will have our completed graph. So now what we need to do is just answer the final question, which is, are these data likely to be reasonably accurate? So, if we look at a graph here, we see that the top three labels, A, B, and C, contribute more than 67% of the total revenue, confirming that a few dominant labels generate most of the income. Now, since these revenue values are reported by large firms, they're most likely to be reasonably accurate, but smaller uh record labels may have underestimated figures. So the conclusion that we can draw is that a few companies dominate the industry, with the top 3 contributing over 67% of the total revenue. The data is likely accurate for large labels, but may underestimate smaller labels. And so that's going to be the answer for the second half of this question. So, I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Pareto Chart

Box Office Revenue

Data Accuracy

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