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Forbes magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least $\$ 5$ per share, and have reported annual revenue between $\$ 5$ million and $\$ 1$ billion. Table 1.37 shows the ages of the chief executive officers for the first 60 ranked firms.

$$\begin{array}{|l|l|l|}\hline \text { Age } & {\text { Frequency }} & {\text { Relative Frequency }} & {\text { Cumulative Relative Frequency }} \\ \hline 40-44 & {3} \\ \hline 45-49 & {11} \\ \hline 50-54 & {13} \\ \hline 55-59 & {16} \\ \hline\end{array}$$
Table 1.37

$$\begin{array}{|l|l|l|}\hline \text { Age } & {\text { Frequency }} & {\text { Relative Frequency }} & {\text { Cumulative Relative Frequency }} \\ \hline 60-64 & {10} \\ \hline 65-69 & {6} \\ \hline 70-74 & {1} \\ \hline\end{array}$$
Table 1.37

a. What is the frequency for CEO ages between 54 and 65?
b. What percentage of CEOs are 65 years or older?
c. What is the relative frequency of ages under 50?
d. What is the cumulative relative frequency for CEOs younger than 55?
e. Which graph shows the relative frequency and which shows the cumulative relative frequency?

(Graph can't copy)

For this question. What told the National training recently started a business providing training events for corporations on in order to better understand the profitably of business, The honor asks you for analysis off the cost work cost of fixed because the variable and so on and you have the following information, which is in the question on then the national training is pleased with the service they used for the Katrine. But then you want the actually to the first question they asked to draw a graph they picked in the fixed cost variable cost total cost for each training vester the number of guests. So we're going to be starting with the first question for that, um, thing. So we're gonna I'm sure drawing the graph that shows the fixed cause variable cause on total cost and from information we're giving me, giving the trainer possession, material possession, catering, cost possession, the food price, the set upon cleaning and the fixed feet. So we're gonna use all the information to find a graph. So the first question graph that shows fixed cost, variable cost, total cost. So the white access and the number of guests to be on the X Ass is on. Why, aunt? Uh huh. So the total cost because I'm variable cost to be on the y toxics and number off guests on the X axis. So that's what we're going to do now. And that should look like this. Then you go this way. So we're going to label these from 0 to 1 50. The white access from 0 to 1 50. So I have 25. We have 50. We have 75 We have 100. We have won 25 and then we have 1 50. And the year we go from 5000 to 45,000. So So we have 45,000. We have 5000. We have 10,000. We have 15,000. We have 20,000, 25,000. We have 25,000, 20,000, 15,000 and 10,000. So now we're going to be drawing the graph. We're going to be starting with fixed costs is in a different colors. So the face class is don't be between 15,000 and 20,000. It is going to be on the street line, and we're going to connect this and next is so this is the fixed costs. The next is the variable cost. You were because last stuff from here, Then we won 15. 20,000 right here. So I'm going to trace this. I'm gonna trace this all the way down there. Okay, so this is the variable cost, and then the next one is the total cost. We're going to connect all this together, and this is a total cost. So this is what the graph looks like. And this side depicts the total cost. Variable cost of fixed costs on this size depicts the number of guests according to what the question tells us. So we're going to move to the next question. Now, suppose 100 people attend the next event. What is the national trainings? Total nets cost on the cost for attendee. So we're going to start there. So the number of attendee is Andre, right? And the national training total net cost would be natural. So I'm going to start with the fixed cost the trainers cost is to finally fisk cost the trainers cost is $11,000. Yeah, the materials from the question right materials is $2500. The fixed fee were given is $5000. So therefore, the total fixed costs will be the addition of all these, and that's $18,500. So now I'm next thing I'm going to do is to find the variable costs for that. The materials, first of all, the materials is $35 and that way we know that the number attend the for this question is 100. So that will be 35 times 100 right? And that's 3500. The kitchen costs. It's still $75 on there under People Times 100 that's 7500 right? The next one is the set up of cleaning costs set up cleaning Coast on that's $25 multiplied by 100 attendees, and that's 2500. So therefore, the total variable cost will be the addition of all this and that 13,500 right? So we're going to, um, subtracted discount by education because we haven't discussed by Katrina so less the discounts. So that's minus 1000, right? And then the total is now going to be 12,500 because of the discounts so moving on we're going to find the total costs, the total cost is going to be cause the total fixed costs plus total variable costs. I'm sorry. Supposed to be T v c. Total variable cost on that equals to go back 18,500 plus 12,500. So the total costs for this question is 31,000 US dollars. So now the class part Andy, Because also supposed to find that the cost Well, I say M d is the total cost divided by the number of attend the attendees on this question in total cost is 31,000, right? Our total number saying this is 100. So the cost part saying this for this question is $310 and that's the answer. Mhm. Now, the next question about three. Yeah. Suppose instead that suppose instead that 1 75 people attended. So instead of 100 people were to solve for 1 75 people, what is the national straining? Total net cost on the cost per attendee. So we're gonna on work that so now for this question and is 1 75 right? So I'm going to do the same thing we basically did for number two, but we want 75. So the national trainings total cost is what we're going to find. So the fixed costs for the fixed cost we're going to first find the trainers caused the trainers costs is 11,000. Yeah, the materials. It's 2500. The fixed fee. It's $5000 on a total, fixed costs will be a cost to $18,500. Now I'm going to find the variable cost we're going to start your mouth. Cereals for the materials is 35 does each multiplied by 1 75 people attending on this is equal to 6001 1 25. The next one is the catering cost, and it's $75 multiplied by 1 75 people, and that's 1 13,025. The next one is a set up off cleaning costs, and that's $25 multiplied by 1 75 people. And that's 4000 375 Now, when you add the total variable cost, you're going to get 6 23,025. But then we have a discounts from the key Tre so we're going to less the discounts on way less these kinds of $1000. The total The total left to be 6 $22,025. That's the answer for that one. So now the total cost, the total cost is he calls to fixed costs those very because, right, So that will be close to 18,500 plus 22,006 to 5. So now the total cost to be 41 1001 $125. So now the next part of the question is the cost. Part n g cost per attendee is equal to the total cost divided by the number off attendees on the total. Of course, we just found is 41,000 1 $25. The number of tenants were given is 1 75 people so cost parts and you we Sonia and $35. And that's the answer for the question. Now, the last part of the question moving on. How should national training charge customers for their services and explain why? So I would say national judicial charges customers according to the cost based pricing metal, and I'll explain why this is because you would have to first calculate its total cost, then put a particle a percentage of the cost as its profit. Imagine rights. So then you and I had the profit margin to the total cost on the song. Opt in will be charged from the customers, for example. Now, in the case where we had 100 home attendees, the cost part and it was 3. 10 on. If you keep the profits percentage as 20% then in profit to be 62. Therefore, the national training issue charge, you know, 372 multiplied by the prophet. Let's be cost about 10 days for this case. So that's why I say to shoot charge, just use the cost based pricing method. So let me just see so it will add the perfect imagine to the total costs and some obtained will be charged from customers. Yeah, so that's it

Okay for this problem. We are given some student some information about most important issues facing young adults and five different categories of issues that they have. And they ask us to make a circle of graft and a bar chart and compare them. So let's start off here by giving this. It was a nice circle. Okay, An amendment that black. But we'll leave it purple, so we'll go there. So, um, circle and it is a little bit of work with percentages, and comfort goes into 360 degrees. So let's 50% with nice about a circle graph is, you know, your fifties and 25 stuff. So if I was going all the way across with the super graph, we would know about it 1 80 away across. But this is 187. Greens correspond to 52% sites on the 1st 1 but the big deal is visually, we can already tell that half a little more than half think that That's the biggest issue there. 52% you, 2%. I think that we need to make better money, okay. And then for the next piece of our puzzle way. No, that's 18% is for strengthen relationships. Okay, a little bit of work had a time. 18% of the same of 65 degrees. I'm gonna estimate 65 degrees here. So my black man and 65 degrees a little sleeps there, nor the numbers on their cause. That's from the horizontal. 65 degrees would be about right there. So for that category, um oh, sure. Pain with his brother. So for that kind of going, strengthen relationships. So that's 18%. 18% think they need to make better money choices. You're strengthen relationships and again see a success to talk about what the photograph is even in the second part, being kind of see proportion wise, you kind of see how important that is by this size of the circle there, the size of the sector of the circle. So let's look here. So the next percentage is 11% which is about 40 degrees. So I'm just gonna estimate here more pathway. So the next piece of our puzzle there, we know that 11% and that the answer for that category is protecting the environment is an important issue to these students, Castle. 9% is environment. And for the next piece, then we drop up Really slivers. The next to be is there 10 and 9%. So you want to make sure this one is this a little bit bigger than the other one? I think my relative sizes air off a little bit here. I made a little fancy work at the end to make him a little more proportional. So let's go over here and which were end. And I think I'm gonna make this piece just a little bit bigger because I want at least show that 11 is bigger than tens bigger than nine. So we draw the sector here, and I don't think your statistics teachers want the most perfect circle in the world. But proportions are important. So make sure this proportion looks bigger and the other next to so that should give us probably want their okay, change of colors. And so, for the 10% is balancing work, importunate personal life, and finally 9% in the last piece of the puzzle. So 9% say important nutrition, perhaps a, uh, party. They want a bar chart. So we use this. Let's look here. So again, we just want to have some What's pretty scaled? Um, so I'm not gonna worry about the precision too much here. Nice fear. And with bar charts were enough space in our bar chart between each of our bars. Categorical data. So gonna have a bar for each of these categories. So pretty much that same color technique we see and see that so better money choices. So let's just use this is 10 2030 40 50. So let's just draw bar chart that's a little bit looked in. 2030 40 50. So there is my better life choices. Okay, so this is about 52% and then strengthen relationship is about 18. So there's 20 a little bit less, and the next one is 11. So it's 10. 11 um, and then they go down to 10 and finally 9% so you could argue a little bit better. You kind of see it. All of the difference in the last few bars a little bit better, but I think generally, um and you kind of lay believes that I'm not gonna be a label. These all out if you want to take the time on keeping your short. But you can basically write each of these words down here for each of these guys here. So right, label each of these categories. Um and let's just make sure we answer the question. So the question was PortSys has compared the appearance of the circle graph with the bar graph in part be so one which one of best represents the relationship between the various issues. Uh, I think the circle graph best really best represents the relationship because of the proportionality ease, which is more than the other one. And you can see parts and holes, so that's pretty much it. You got your strip a graph, you got your paragraph. I am going to just take it another second here to label this officer will get our 50% and we're 25% and again, I'm not gonna list is all out because of the business of the graph. But what you would want to do is you want to label each of these titles down below here, and there's are two different drafts


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