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The total income for white households making under $\$ 250,000$ in 2008 is given in the following table. Source: U.S. Census Bureau.

a. Use this table to estimate the mean income for white households in 2008.

b. Compare this estimate with the estimate found in Exercise 39. Discuss whether this provides evidence that white American households have higher earnings than African American households.

$\$ 64,430$

Multivariable Optimization

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Johns Hopkins University

Missouri State University

Harvey Mudd College

Baylor University

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