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# Inductive & deductive reasoning

Sal discusses the difference between inductive and deductive reasoning by considering a word problem. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Think about this real
world problem. To estimate the population of a
town in upcoming years, one of the town workers collected
populations from past years and made this table. So they have years starting
with 1950 and going up by increments of 10 years. And they just figure out the
population of the town in each of those years. The town wants to estimate
the population for 2015, 2018, and 2020. To do this, will you be using
inductive reasoning or deductive reasoning? Now before answering that, let's
just think about what inductive reasoning is and what
deductive reasoning is. Inductive reasoning is looking
for a pattern or looking for a trend. So it's looking for a trend
or a pattern and then generalizing. You could imagine, it's kind
of extrapolating the information you have,
generalizing. Deductive reasoning is taking
some set of data or some set of facts and using that to
come up with other, or deducing some other, facts
that you know are true. When you generalize you don't
know necessarily whether the trend will continue, but
you assume it will. You don't know 100%
it'll be true. With deductive reasoning,
you know it'll be true. You're starting with facts. And then you're deducing other
facts from those facts. Other facts that you
know are true. Now, when the town is
estimating, and that's kind of a clue that they're not going
to know the exact population for 2015, 2018, and 2020. But when they estimate the
population for these years, these years are in the future. They don't know what
the population will be in those years. The best they can do is see
the trend of growth here, maybe see what percentage it's
growing every 10 years. Or what the absolute number of
growth is every 10 years. And maybe they can continue
that trend out to 2015, 2018, and 2020. So they'll be looking for trend
in growth over this 60-year period. And then they'll generalize
it out to these years. So this will be inductive
reasoning.