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