If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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

Defining appropriate quantities for modeling

CCSS.Math: ,

Video transcript

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 are hiring writers and 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 will 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 just spend expenses on things like rider 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 left over well some people would argue the whole point of a business is to generate that profit that is an outcome you want to maximize as an output and so I would consider that an output and so the question of per activity 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 riders 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 ten thousand dollars for five riders so it would be two thousand dollars profit per writer and what would be what would be bees per activity by this definition well twenty eight thousand dollars divided by eleven twenty eight thousand divided by eleven riders those twenty eight thousand dollars in profit that case this is two thousand and we'll around two thousand five hundred and forty five so approximately two thousand five hundred and forty five dollars of profit per writer so based on this measurement of productivity it looks like website B is more productive now what if we do 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 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 a hundred and ten divided by five which would be twenty to twenty-two posts per writer and website be two hundred divided by eleven two hundred divided by eleven gets us we old ik adjusts around that to maybe eighteen since we want to get rough estimates to eighteen 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 post posted times the average number of posts you take that quantity and then maybe add the average likes per post or multiplied by the average likes proposed and then add to that the comments per post or multiplied by the comments proposed and then divide by the number of writers or the number of writers and the expenses or divide just by the expenses but the general notion is you want to divide some you want to 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 want to combine how do you want to mathematically combine those outputs and inputs