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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 3: Problem solving and data analysis- Ratios, rates, and proportions — Basic example
- Ratios, rates, and proportions — Harder example
- Percents — Basic example
- Percents — Harder example
- Units — Basic example
- Units — Harder example
- Table data — Basic example
- Table data — Harder example
- Scatterplots — Basic example
- Scatterplots — Harder example
- Key features of graphs — Basic example
- Key features of graphs — Harder example
- Linear and exponential growth — Basic example
- Linear and exponential growth — Harder example
- Data inferences — Basic example
- Data inferences — Harder example
- Center, spread, and shape of distributions — Basic example
- Center, spread, and shape of distributions — Harder example
- Data collection and conclusions — Basic example
- Data collection and conclusions — Harder example

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# Data inferences — Basic example

Watch Sal work through a basic Data inferences problem.

## Want to join the conversation?

- Will Sal take away the old SAT practice after January?(8 votes)
- I doubt it. The old SAT has its values and I wouldn't think Sal would remove all the work he did with making videos of all the practice problems.(15 votes)

- An easier way: Cross multiply, do 399 x 635k then divide all over 1500. the number in your calculator becomes 168, 910 which is closest to D(11 votes)
- I agree and tried the same cross multiply method and I got the same answer, if this on the calculator ok part it would have taken a few seconds to solve.(3 votes)

- Honestly, with a calculator, I found it easier to just multiply the proportion(399/1500) times the population (635,000)(8 votes)
- Can we use a calculator for this part? Because that would make finding the answer super quick here.(7 votes)
- Anyone for august 26?(7 votes)
- how do you know to set it up like that? 399 over 1500?(2 votes)
- If we want to get more technical and forget about Sal's way of solving the problem, it's not really important whether it's 399 over 1500 or 1500 over 399 (although 399 over 1500 makes more sense) the important part is that when you know which belongs with what.

1500 is with 635000, because both of them represent the whole group, so:

133/1500 = x / 635000

And to solve for x:

133/1500 * 635000 = x (this is where 133/1500 * 635000 came from)

Likewise, if you somehow decided to use 1500/133, then:

1500 / 133 = 635000 / x (remember, 1500 and 635000 must be in the same level, in this case numerator)

Solve for x:

1500/133 * x = 635000 (first we bring x to the top by multiplying both sides by x)

x = 635000 * 133/1500 (then solve for x, like a normal equation)

And if you have noticed, both methods lead to 63500 * 133/1500, but the first one is easier (in this case) and makes more sense. In ratios and percents, we usually write part / the whole.

Hope this helped.(10 votes)

- why is the example always easier than the task?(6 votes)
- At1:45, Sal sir rounded off 399, but in case if the options are not too much ranging so is it ok to this ronuding off thing.(2 votes)
- Yes. Notice that it
**says**approximately, so you will have to round anyway.

400/1500 = 0.2667

399/1500 = 0.266

That is a difference in the ten thousandth place, so you buy a LOT of time by rounding and you do not lose much at all in accuracy.

The "real" answer using 399/1500 is 168,910

and the estimated answer is 169,333.333

The`estimated`

answer they gave in the options is 169,000 with the closest contender 127,000 which is way too small to be tempting.

So, your rounding doesn't cause you to lose anything, except extra seconds or minutes of messing around with the "real" numbers that are harder to work with.(5 votes)

- Is every math question now formatted as a word problem?(2 votes)
- no not every math question is formatted as a word problem. Sal just wants to use more real life situations and not just plain numbers.(4 votes)

- the level of math in sat would be same like the above question because I am little weak in data infrences(0 votes)
- In the real SAT, there would be much more difficult questions compared to this one.(6 votes)

## Video transcript

- [Instructor] In a
survey of a random sample of 1,500 residents aged 25 years or older from a particular country, 399 residents has a
bachelor's degree or higher. If the entire county had 635,000 residents aged 25 years or older, approximately how many county
residents could be expected to have a bachelor's degree or higher? All right, so we have this random sample. We randomly sampled 1,500
folks aged 25 years or older. We find out that 399 of them have a bachelor's degree or higher. So of our sample, 399/1500ths
have a bachelor's degree. Now the entire county
has 635,000 residents aged 25 years or older. So when they're saying approximately, so we're gonna estimate here, how many residents could be expected? Well, since this was a random sample, you would expect that the same fraction of the random sample, that that would be approximately the same fraction of the general population
aged 25 years or older that would have a
bachelor's degree or higher. So we could just take this
fraction and multiply it times the entire population
to have a good estimate of, or good expectation, for the total number of folks with a bachelor's
degree or higher. So we could just multiply this. Now there's two things going on. We really just want to
get an approximation, and the good is, we have multiple choices right over here, and these
are fairly spread out, so we could round some
of these numbers here to simplify this a little bit. So this is going to be
approximately the same thing. 399 is awfully close to 400. So it's gonna be
approximately 400 over 1500 times 635,000, 635,000, and that's approximately
the same thing as, let's see, four over 15. If I divide the numerator
and denominator by 100, times 635,000, 635,000. Let's see, I could
multiply all of this out if I want, but this
quantity right over here, that's gonna be, so this is what we're, if I could just, we could
figure what that is, but once again, we're just approximating. So this is gonna be greater than, if I just made this a 600,000,
and I'm just gonna do that, just 'cause it's kind of close to 635,000, and 15 goes into 600,000 nicely. So whatever quantity this is, this is going to be greater
than four times 600,000 over 15. And once again, I went to 600,000, just to make my math a little bit easier, and because 15 goes into
600,000, nice and easy 'cause 15 goes into 60 four times. So if you divide the numerator
and the denominator by 15, this becomes a one, and
then this becomes 4,000. I'm sorry, 40,000. Instead of 600,000, you're at 40,000. So this boils down to,
maybe I'll cross out this, this is 40,000. So it's gonna be four times 40,000, which is 160,000. So our approximation is gonna
be greater than 160,000, and there's only one choice
here that is greater 160,000. And if you were multiply this out, you would get even closer to 169,000.