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

Use the table to estimate the mean income for African American households in 2008.

$\$ 45,794$

Multivariable Optimization

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this is question shows is a frequency table for incomes of African American families whose salaries are less than 25 $250,000. It wants us to find them mean salary or at least estimated using this frequency table. We know when we're estimating means from frequency tables, that X bar is equal to the sum of the value times frequency divided by the sum of the frequency. Now in this table that what is being counted is the ranges. So we don't exactly have a new X, but we are given the midpoint of each range. And so we'll use that as X. So I'm gonna write down ah, small part of this table and we'll go from there. I'm gonna write the mid point, But instead of ready as, uh, just dollars, I'm gonna ready. That's thousands of dollars. It'll make things a little bit easier simply to read. So the first entry is $10,000 then 30,000, 50,000 70,000 90,000 125,000, 175,000 and 225,000. Then we have frequencies we have. And this is already in thousands, Really? So This is really 4,378,000 3,891,000 2,500,000 1,497,000 866,000 998,000 309,000 and 79,000 Now I will make a column for X Times f. This is just going to do in a calculator. I'll multiply my ex Colin Times my f column Get 43,007 or 80 116730 125 1000 104,007. 90. 77,000 940 124,750 540. 54,000 75 in finally 17,000 775 All right, so now that I have all of this, I've got all of my ex efs and all of my efs. All we need to do now is some them up. So I had another row for our sums. Now we don't really care about the sums of our mid points. MENSA doesn't really matter, but the sums of our efs if we add the's old up, we get that there are 14 million. Remember, this isn't thousands. 14 million, 518. And when we some of all our x times efs we get 6,664,000 840. And so now we've missed around with the units a little bit. Do we have to change anything before we do our division? Well, no, because this is in the units on the some of f here is in thousands of people. The units on X Times F oh are thousands of dollars. So it was right kay by thousands of people. So when we divide r X f by X, everybody, some of f will get thousands of dollars, thousands of people divided by thousands of people, and we'll be left with just thousands of dollars. So let's go ahead and do that. X Bar is going to be 664 1008 $140,000.1000 people's divided by 14,518 1000 people, and we'll get that explore is 45.79 for $1000 or all right, a little bit more neatly, $45,794. That is the an estimate of the mean income for African American families making less than $250,000 a year. That's your friend.