WEBVTT
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this question shows is a table of the ah,
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frequency table of incomes for white families making under$250,000
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a year. Now we know what we're finding.
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Estimating a mean he's in frequency table. We have
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that the mean explore is equal to the sum of
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the value times the frequency over this some of the
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frequency. Now here we have ranges as our values
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. So that means we need to take the midpoint
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. Luckily, the midpoint actually already included in this
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table. So we're getting so I'm gonna copy down
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part of this table. Um, and we'll add
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on to it and do some calculations from there.
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So for X R value, I'm not gonna write
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down the whole number. I'm just gonna write down
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the number in thousands of dollars. So first we'll
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have 10 then 30 then 50 70 91 25 1
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75 and 2 25 Then we have our frequency.
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Enough of frequency. Um, all right. Down
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the whole thing. This is already in thousands of
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people. So it'll be 16,241 which is really 16
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million to 41 1000. That will have 20,047,000 16,065,000
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12,746,000 nine million 80,000 12,230,000. 4,000,014. 98 1000
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and finally 1,743,000. So next I'm gonna make a
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column called X Times F and I'll just multiply these
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two columns together to give us to think that we
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need to sum up X times f will get 162,410
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and 614,610 then 803,250 then 892 220 817,000. Tune
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200. Uh, 5 1,529,000 750 787,000 150 and
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finally 392,175. Now, since rotate. Since we're
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doing the average, which requires this sums of f
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, x, f and F, I'm gonna just
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add a new rule where I sum up these columns
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. We don't really care about the some of X
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that doesn't help us out here. And the sum
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of F Replagal this door calculator will get, Ah
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, 93,000 90 which is really 93 million. Remember
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, um, 93 million people, and then when
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we do, the sum of X times f will
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get 5,997,000 765. So now all that's left to
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do is to find X bar. We just need
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Teoh divide the sum of except by the some of
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F and we'll get at 505,997,007 or 65 divided by
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93,000 90 is equal to 64.4 to 9. Now
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, remember, I've wrote our X column in terms
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of thousands of dollars, so are mean is also
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gonna be in thousands of dollars. So, really
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, what? This means that the meeting or the
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mean income for white families making less than$250,000 a
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year, is$64,000.400 29 now, the next four
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tasks. Um, is this enough evidence to show
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that, uh, black families make less than white
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families in the previous question? We So we saw
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that the mean income for black families making less than
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$250,000 was only 45,000 794 dollars. So this is
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significantly less now. What can we say from this
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data? Well, it's important. First, to
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remember our scope. We looked at families making less
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than$250,000. So inside this scope that is,
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out of all families making less than$250,000. It
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is true that black families often make less than white
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families. Now, if we had more data about
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more families, we might be able to generalize to
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all families. But the data that were given and
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the methods that we used did not allow us to
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, uh, conclude that about all families, and
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so that is your finally