Problem 25 Hard Difficulty

Table 1.8 shows a data set containing information for 25 of the shadow stocks tracked by the American Association of Individual Investors. Shadow stocks are common stocks of smaller companies that are not closely followed by Wall Street analysts. The data set is also on the website that accompanies the text in the file named Shadow 02.
a. How many variables are in the data set?
b. Which of the variables are categorical and which are quantitative?
c. For the Exchange variable, show the frequency and the percent frequency for AMEX, NYSE, and OTC. Construct a bar graph similar to Figure 1.5 for the Exchange variable.
d. Show the frequency distribution for the Gross Profit Margin using the five intervals:
$0-14.9,15-29.9,30-44.9,45-59.9,$ and $60-74.9 .$ Construct a histogram similar to
Figure 1.6 .
e. What is the average price/earnings ratio?

Answer

a. 5 variables
b. CATEGORICAL=Exchange, Ticker Symbol
QUANTITATIVE=Market Cap, PricelEarnings Ratio, Gross Profit Margin
c. See bar graph
d. See histogram
e. 20.216

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Video Transcript

All right, so in this problem, we are given information about 25 Uh, what are called Shadow stocks. So I guess lesser known stocks and we're given some information about them. So the first question says how Maney variables are there. And so I just took these headings from the table and brought them over, and we can see that there are six different variables or six different pieces of information that we are given about each of them. So Part B says okay, which of those identify those variables as either categorical or quantitative. So categorical means non numerical data or like categories. So, uh, this the company name? That would be a category. The exchange. So that's like of it's on the American Stock Exchange or the New York Stock Exchange. Er, something else. So those air categories as well the ticker symbol is literally a symbol, so that would be a category. And then we get to market cap and it's in money and millions, so we can tell that this is going to be numerical data. So its quantitative same thing price earnings ratio, is going to be new. Miracle. Um, it's expressed in ratios is so quantitative and then the gross profit margin. These are expressed in percentages. So again, we are dealing with quantitative data. So we have three categorical and three quantitative in part C says All right, make a graph of the information that is in the exchange column. So in this exchange column, we have three different categories of exchanges. We have, um a m e x. We have O T C or M I S e the New York Stock Exchange. And then we have one of the one that's called OTC, And I went through, encountered up how maney there were of each. So for the a m e x, there were five of the 25. We're, um that exchange and why SC There were three and the rest of them were all OTC. So if we take those and we convert them to percentages five out of 25 it's going to be 20%. So that 0.2 and then the New York Stock Exchange, three of them corresponds. Then, too 0.12 or 12% and then 17 of the OTC. Um, that translates to 68%. And we're being asked to make a bar graph. So a bar graph is a pretty straightforward graph, and I'm gonna use this column to represent my percentage is my, um my frequencies there. Um, so this would be the frequency, and I'm gonna count squeeze another one in here to keep them pretty evenly spaced. So if this is 10% this is 20%. Um, 30. This would be 40% 50. This would be put 6 70.8 And since my highest number is 68% I don't really need to go any higher than that. And then I'm going to have my three variables my three categorical variables, and I'm just gonna make a bar up to that frequency for each of them. So for Amex, Niko ups 20%. And there's my bar. New York Stock Exchange is only 12% so it's gonna be a little bit lower, but above 10%. So there we go, and then OTC, is it 68%. So almost up to here, by estimation, going to be the height of that bar when we have our bar graph. Okay, so moving on then two part D. Um it asks us to set up a frequency table or or find out based on some different intervals to look at the gross profit margin, this category, this category right here and break it down. And I've done that. So I've made my frequency table and I've gone through and tell it up and counted. How many of those different companies had a gross profit margin within each of these intervals? And these are the frequencies that I counted There were to between zero and 14.9 six between 15 and 29.9 eight between 30 and 44.9 six and then three. And so these frequencies. So something was like 14.9. It would go into this category as soon as it hits 15. It would go into the next interval so that I could use these. Now I'm dealing with quantitative data. So now I could make what's called a hist a gram. One of the features of a hist a gram is that the bars have to be connected and that this scale has to be continuous. So we just made the bar graph earlier, I was using categorical data on my horizontal axis. So those bar should not be connected. And they could have gone in any order on that graph. Whereas these numbers have to go in order from smallest to largest. So I'm gonna put the bars in there and from zero, which is my vertical access to 15. My frequency is to someone to draw the bar all the way over to 15 so that the bars going to connect and then from 15 up to, but not counting 30. My frequency, It's six. So I'm gonna go up to six and over and then all the way down the 30. So no gap between the bars from 30 up to 45 not including 45. Gonna go up to eight and then back down from 45 to, but not including 60. I have gonna be the same height here, so I'm gonna bring that far down pretty close. And then I have three in my last category between 60 up to, but not including 75. So there's my nice Ah, very symmetric. I'm nice. And, you know, uh, evenly distributed history. All right. For the last question, we are asked to calculate the mean of or the average of the price, um, earnings ratio. And I'm just going to abbreviate that p e ratio. So let's recall the way you find the mean is you find this some of all 25 p e ratios, and then you divide by the total number of companies or the total number of entries we're gonna right cos because that's what these air representing. So when I added up my my calculator, I just added up all the numbers. It turns out that all of the P E ratios come out to be 500 from five 0.4 and there were 25 companies. So when I divide that, I find that the mean P E ratio is 2.216

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