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Current time:0:00Total duration:6:11

Defining appropriate quantities for modeling

CCSS.Math: ,

Video transcript

- [Instructor] So I have data here on two different websites, website A and website B. And my question to you is, which one is more productive? And some of you might be asking yourself, what does it mean to be productive? And at a very high level, you could view productivity as how effective something is at producing. So for a given amount of input into the process, how much output are you getting? If you want to get a little bit more exact, you could view it as the rate of output per input. But that still makes us ask the question, what are the inputs and what are the outputs? So pause this video and think about how you would measure productivity for or how you would compare the productivity of these two websites. And there's multiple ways to do it. All right, now let's think through it together. What I'm first going to do is look at each of these lines and think about whether they are an input or an output. So the number of writers, well, you need the writers to produce the website. So I would consider that an input. Although if you were the head of HR, the person who is hiring writers, the head of human resources, and you were hiring writers, then that could actually be an output. But if we're just thinking about creating a website, we need writers to create it so that's an input. Number of posts posted, average number of words of post, average likes of post, average comments of post, number of new subscribers, those all feel like outputs. If the writers do a good job, they're going to produce a lot of posts, they're going to, I guess, have a lot of words, I don't know if it's good to always be wordy. People will like their posts, they'll comment on those posts. We'll have new subscribers. So this is all output. What about revenue? That's how much money a site brings in before having to pay its expenses. So that also should be an output because if the writers do a good job, if the site is well run, they will generate a lot of revenue. What about expenses? Well, you need to use expenses. You need to spend expenses on things like writer salaries in order to create your website, in order to generate that revenue. So I would consider that an input. And what about profit? Profit is all the money you bring in minus your expenses and how much you get leftover. Well, some people would argue the whole point of a business is to generate that profit. That is an outcome you want to maximize, an output. And so I would consider that an output. And so the question of productivity really just boils down to which output or what combinations of output do we want to figure out the rate that we're generating relative to some input or some combination of inputs? So a really simple way of measuring productivity in this situation, let's define it, productivity. And once again, there's multiple ways of defining it. Let's say it is equal to the profit per number of writers. So it could be profit over the number of writers. If we define it that way, which website is more productive? Well, website A, in that definition, A would have a productivity of $10,000 for five writers. So it would be $2,000 profit per writer. And what would be B's per activity by this definition? Well, $28,000 divided by 11, 28,000 divided by 11 writers, there's $28,000 in profit. That gives us a 2,000, and we'll round, 2,545. So approximately $2,545 of profit per writer. So based on this measurement of productivity, it looks like website B is more productive. Now what if we did maybe even a simpler one, or maybe one that you might think is even more natural? What if we thought about it as the number of posts per writer? So let's do it that way. So if we just defined productivity, I'll just do that, as being equal to the number of posts divided by the writers. Well, in this situation, website A would have a productivity of 110 divided by five, which would be 22, 22 posts per writer, and website B 200 divided by 11 , 200 divided by 11 gets us, well, we could just round that to maybe 18, since we want to get rough estimates, to 18 posts per writer. So by this measure of productivity, website A actually looks more productive. So hopefully this gives you just a general sense of what productivity is, and an appreciation that there's multiple ways of measuring it. And you could do much fancier things, you could say, you could make it a whole combination of outputs divided by a combination of inputs. So you could define productivity as the number of posts posted times the average number of posts, you take that quantity, and then maybe add the average likes per post or multiply by the average likes per post, and then add to that the comments per post or multiply by the comments per post and then divide by the number of writers or the number of writers and expenses or divide just by the expenses. But the general notion is you wanna take some combination of the outputs, maybe even just one output and divide it by some combination of the inputs and you can actually decide how you even wanna combine, how you wanna mathematically combine those outputs and inputs.