1.6: Practice and Exploration
- Page ID
- 56726
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- One of the new jobs for the new millennium is that of an influencer, an individual who builds an online presence through engaging content like photos, videos, and updates. Influencers differ from traditional celebrities because they grow their following through social media rather than preexisting fame. Successful influencers are often paid by businesses for to promote products and services. For example, influencers have commonly worked in the fashion industries. Of course, for a business that is considering hiring an influencer, the relevant question is how much they should be paid. Discuss the type of data that the influence might provide to the business that would help the business decide how much the influencer would be worth in terms of their profits. What potential problems might exist with the data? What types of data could the business find on their own?
- Suppose that you are interested in attempting to make a prediction about an upcoming soccer match. You would like to make the best prediction possible about the outcome, so you need to start thinking about the data you will use to make your prediction. What type of data might you consider when making your prediction? Where would you look for the data, and do you think that all the data you would be interested in is easily available? Given the best data that you could find, how accurate do you think your prediction might be? What could happen during the game that would make the data you collected less relevant to the outcome of the game that you might have assumed when you made your prediction?
- Suppose you are considering opening a new business in your local area. For you to obtain financing from a bank, you must provide a business plan, and you must be able to demonstrate that there will be demand for the services that your business provides. What type of data might you consider gathering that will support your application for financing? Is this data readily available? Where do you think you might be able to obtain the data? What problems might you face in gathering the data that you need?
- You are planning an outdoor event that will take place six months from now. The event will only run smoothly if the weather is reasonably warm and dry. If there is inclement weather, you will personally suffer a substantial financial loss; if the weather is nice, you should get a large financial gain. You are considering insuring the event. That is, for a fee an insurer will provide a payout to you if the weather is bad on the day of the outdoor event. What types of data do you think that the insurer would consider in deciding how big the fee should be?
- Suppose you are considering purchasing a new automobile. You have narrowed it down to a single model that has three options: gasoline powered, hybrid powered (electric with gasoline backup when needed), and fully electric. What type of data should you consider when trying to decide which option to purchase? How would you gather this data? What types of problems might you have in finding the data you need? What type of things could happen after you make your purchase that would have changed your decision had you known they would occur?
- Suppose you oversee your campus activities board, and you have been asked to book the hot new band called the “Probability Twins” for an on-campus concert. You will need to determine what price should be charged for the tickets. What type of data should you consider when trying to decide what the ticket price should be? How would you gather this data? What types of problems might you have in finding the data you need?
- Suppose you are flying to Hawaii for a much-needed rest after a long semester. You need to be at the airport by 10:00 a.m. so that you have time to check-in, go through security, and reach your gate within the required time. Using your own home and local airport as a model, what type of data should you consider to decide when you should leave your home to get to the airport on time? How would you gather this data? What types of problems might you have in finding the data you need?