Comparing guesses and absolute errors
At about 65-68s the narrator says '343 is 3 less' than 350, but later plots the point as 347 with error 3; the portion is 347 g (343 would be 7 less). Interventions use 347.
The check-ins use the correct version. The video is Khan Academy's, unchanged.About this video
A baker aims for 350 g dough portions, and the video finds each portion's absolute error: its distance from 350 g, always non-negative. It then plots portion size against absolute error, and the points form a V shape with slopes of -1 and 1 meeting at 350 g.
You'll be able to
- calculate absolute error as the distance between a measured value and a target.
- make a scatter plot of values against their absolute errors.
- explain why a plot of absolute error makes a V shape.
Key words
- absolute error
- How far a value is from the target, always counted as a positive number (or zero).
- scatter plot
- A graph of separate points, each showing a pair of values.
- target
- The goal value; here, 350 grams per dough portion.
Transcript
- [Tutor] A baker sets a goal of 350 grams for each portion of bread dough. In a certain baking session, portions have an absolute error that is less than 15 grams. The table represents their portions, all right, we have some blanks here. And let's see, it says fill in the missing absolute errors and then create a scatter plot that represents the portions and the absolute errors. So why don't you have a go at that and then we'll do it together.
All right, the absolute errors, the way you're going to calculate it is you're gonna see how far the actual value is from the goal, from the target of 350 grams. And it's always going to be positive, we're talking about absolute error. So we're just thinking about the distance from 350 grams.
So we're not going to have any negative values here. So notice, 355 is 5 more than 350. 338 is 12 less than 350. 363 is 13 more than 350. 350 is exactly 350. 341 is 9 less. 343 is 3 less. 344 is 6 less. And then 358 is 8 more. So those are our absolute errors.
And then create a scatter plot that represents the portions and the absolute errors. All right, so let me make an axis here. I'm not gonna go from 0 all the way to 360 just because everything will get clumped around. So let's just focus on going from, I'll put on the X axis here.
I'll put an arrow in both directions here. And this is going to be our dough portions, portion, in grams. And let's see, we're going from, well, let's see, everything that is, well, we said it's within 15 of 350. So let's put 350 right at the middle, 'cause that's our target, 350.
And let's say that's 355, 360, 365. So 365, 355, 360. And then let me do, so this is 345. This could be 340. Apologies if you hear my barking dog. Hopefully, it's not coming up on camera. This is 335 right over there. And then we are going to look at the absolute error can go from 0 to 15.
And so let me put an axis here. I'm not putting this axis right at 0. So let's just say that this can go up to 15, so this is gonna be 5, 10, 15, just like that. And this is absolute, absolute error in grams. So don't get this confused with me putting this at 0, I'm just starting this right at 335 so it's a little bit awkward, like that, but get the point across.
So we have the point, at 355 dough portion we have an absolute error of 5. 355, 5, that's that point right over there. 338, 12, 338 is right around there, 12 is right around there. We have 363, 13. 363, and 13 is right about there, just maybe a little bit to the right of that, 363, 13.
350 and 0 is going to be right here. And then 341 and 9, 341 and 9 is going to be right about there. 347 and 3, 347 and 3 is gonna be right about there. And then 344 and 6, 344 and six is going to be right there. 358 and 8, 358 and 8 is going to be right around there.
And so there you have it, I have the scatter plotted. It makes sense that what you have is, essentially, it looks like a V, like this. And it makes sense because as you have lower values, when you have really values below it, you have a higher absolute error. And as you get closer and closer, you have a lower and lower absolute value or absolute error.
And this has, essentially, a negative slope of 1, and this has a positive slope of 1. So hopefully, this makes sense. But there you have it. There's the scatter block.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.