WEBVTT
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this question asks you to use a frequency table to
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find the mean of a set of data. Now
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the set comes from exercise one, and A Nectars
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has one and three. We created two different frequency
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tables. So part a of this question asked us
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to use the first frequency table that we made.
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Now, keep in mind when we're finding means from
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frequency tables like this, these air only estimations of
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the means the value that we get will depend on
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how we group the data and we might get different
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answers accordingly. The first frequency table used groups from
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0 to 24 size of 25. It looked like
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this 0 to 24. 25 to 49 52 74
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75 to 99 100 to 1 24 and 1 25
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to 1 49 So those are our ranges. We
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had frequencies which will call F of four, eight
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, five, 10 five Earth exceeding four and five
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. Now we know that using a frequency table to
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find them mean we're gonna use is the equation.
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Export equals with some of X times F that is
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all of the values times their respective frequencies over the
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sample size and the sample size. And it's just
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gonna be this sum of all the efs. So
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we have the EFS here, but we don't actually
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have the exes. We have ranges here, but
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to find the X is the values. This method
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asks us to take a midpoint of the range,
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so I'm gonna go ahead and get the midpoint of
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all these ranges. Will have 12 37 62 87
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112 and 1 37 Now we have X and F
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, but we need to find x times f.
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I'll make another column on our table and we'll put
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in the X Times EFS 12 times four is 48
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37 times eight is 296 62 times five is 310
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87 times 10 is 8 70 112 times four is
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448 and 1 37 times five is 685. So
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now we have all our X times, efs and
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all of our efs. The only thing left to
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do now is to sum them up. I'm gonna
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create a some row, and we don't really care
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about the some of the values because they don't That
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doesn't represent all of our data. And we can't
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some up these ranges. But we do care about
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the some of the f con their frequencies when we
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add all these up. Or if we just count
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the number of data points in that table, we
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find that there are 36. And then when we
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sum up all of the X times efs, all
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of the data times their frequency, we get value
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of 2657. So now we know that the some
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of XM's F is to 657 and in, or
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the some of the EFS is equal to 36.
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So that means X bar are mean. He's gonna
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be 202,657 divided by 36 or 73 0.81 As just
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a estimation, dismal approximation. They're a lot more
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, uh, decimals. After that says one way
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of finding the mean using frequency table. But we
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also created a separate frequency table. Um, that
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we're gonna we can take a look at Let me
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scroll down here and I will. Right are other
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frequency table in this one. We use bin widths
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of 20. So we went from 0 to 19
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. 20 to 39. 40 to 59. 60
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to 79. 80 to 99 100 to 1 19
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1 22 um, 1 39 and 1 40 to
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1 59 So I'm also gonna write down our mid
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points this time. Our mid points. Don't line
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up exactly how we like. We'll have a 0.5
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in them. So are good points or 9.5.
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29.5. 49.5. 69.5. 89.5, 109.5 129.5
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in 149.5. Remember, those are X values Wilson
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into Ridenhour frequencies. We found these in problem in
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. Problem, actually, is three remember it?
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It is 45 for 59 three for two. Those
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are frequencies. Now, let's do the same thing
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. We did what we find x times f extents
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f here. Um, your first column is gonna
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be 38 then 147.5. Then 198 347.5 805.5 328.5
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5 18 in 299. So, like we did
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with before, we will add a totals column at
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the bottom. Doesn't matter what the values their total
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to can't add up the ranges again, our frequencies
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will total up to 36. Makes sense. There
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were 36 data points to begin with. That can
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ever change, but now our, uh, our
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X times fl use some of to something a little
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bit different. Now, when you add them all
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up in a calculator, you get 2682 so a
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little bit different. And to find the mean this
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time will do 2682 divided by the total frequency 36
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we'll get something different. We get 74.5. So
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again, these are just ways to estimate the means
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using, um, frequency tables, their estimates because
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they're not always gonna be perfect here. We estimated
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that it's that it's 74.5 above. We said 73.81
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um the true mean is actually somewhere in the middle
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, I think, Uh, yeah, 73.86 So
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it's not perfect, but it gets you pretty close
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, and that's that is your final answer.