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encontro
on-line
matemática
aplicada
computação
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00:00:22
eh
00:00:44
Hello everyone, good
00:00:47
evening, are you listening to me well?
00:01:04
So let's go guys, I think we're going,
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okay, so you're
00:01:09
listening
00:01:10
perfectly well, guys, let's go,
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let's start our little lesson
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today, I'm going to introduce myself first, right?
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I'm the tutor teacher,
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Carline, I'm with you other
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teachers with kess with Felipe with
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liis, right? Then I present other
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teachers also together in the subject
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of mathematics applied to computing,
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so, right, we have some topics to
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cover here in our subject and
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today is an interesting moment, right, for
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everyone, let's address some
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questions, let's also see some questions
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about the work, right, in fact about the
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organization of the groups, I think it's
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important that we capitulate this part
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because we're already approaching the
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final period, right, to
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register for the teams, it's important that
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we recapitulate these aspects too,
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then we will revisit some
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content from week 4 and week 5,
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let me give you my little material
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here to guide you, right? Then I will
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show you some exercises that
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are covered in the book and I also brought
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another one that can help you with
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understanding of some aspects So
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as you know we have a
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limited time here on our
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broadcast so obviously we
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can't cover all the topics that
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are covered in two weeks because it's a lot
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but I brought up some that I think
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are important and are very common or
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bring some other applications of them
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too and at the end, right, I have one more
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invitation to make to
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you, so let's go guys, right, just
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recapping our agenda, I will
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now quickly explain the dynamics of the
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groups and we will talk about the contents
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of week 4 and week
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5, beauty in relation to the dynamics of the
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groups. Guys, you can take the time to
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register within the
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discipline of each of you. It's
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important that you are aware
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of the information that there can only be four
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members per team, but what what's
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more, the system won't even
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let you
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access it, so it's important that you, you know,
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have a
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maximum of four in the group contract.
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any change of team,
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right, or group that you think is
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necessary And these changes must be
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communicated, right, and made by the week,
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it's also important that you, right, If
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there is any situation, report it to the
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Professor or tutor about
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any lack of participation by the
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members. If there is someone who is
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there in the group but did not have any
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contribution, then it is important that there is
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this communication so that we can
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also intervene in some
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way. Remembering that everyone must be
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registered in a
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team only in this way that will open
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the option for you to do the delivery of the
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activity So if you did the
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activity, you were not included
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in any team, you will not be
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able to deliver the activity
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you carried out So this information is very
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important, right?
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between
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you and remembering that you
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will only be able to form teams with people from
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your class, so be aware of
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the class number, if it is final
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1 2 3 4, right, be attentive to this
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information and you can only form a team
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with these people from your class
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also remembering that each team
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will only deliver one piece of work, so there
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is no possibility of you doing
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two jobs and delivering them separately,
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the team is assembled, four members were there,
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something happened,
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someone did it separately, you can't, right, you're just going to
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do the job. delivery of work there
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by
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team, beauty guys, so these are the
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warnings in relation to
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group dynamics, so it is important that you
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are aware of this information,
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I believe that at some point you must
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have already done teamwork, so
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these rules are always very
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important, right, talk to
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your colleagues, maintain a good coexistence or
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do work in a personal group, he's
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there for a reason, so you exchange
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ideas with your colleagues, right, as we
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always say, four heads are better
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than one, right, so it's important that
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you have this communication with your
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colleagues because you will be able to
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exchange ideas. While you have
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any doubts and you can ask
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your teammate, look, I
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had this doubt here so maybe
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that's what I'm thinking, right? So it's
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interesting. this exchange that you have and
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As I said, there is group work, it
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exists for some reason,
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but that was it guys, so let's go,
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let's go to our
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subject content Guys, you must have seen
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that we have a lot of content in
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weeks 4 and 5. several aspects that are
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covered, I will start with you talking
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about
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dispersion measures, how you should intervene, right?
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mean value or the median so when
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can we use these measures
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of dispersion first we can
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use this to evaluate
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data constancy So as deviation the
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standard can help determine
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how close or far the
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data points are from the average if the data has a
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small dispersion this
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suggests that the values ​​are grouped
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around the Average on the other hand if
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we have a greater dispersion of these
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data it indicates a wider distribution
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So through these
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dispersion measures we can also achieve
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this purpose which is to evaluate the
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consistency of the data, to understand how
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that data that we are
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observing, right, that is very important,
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in the profession that you are going to pursue, you want to
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then do some research and move on to
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something like the master's degree, doctorate,
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you will also probably work with
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this, so you are some of the ways in addition
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to what you have already seen in the book
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that can be
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used can also be used to
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compare data sets, so
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when we compare two sets of
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data the dispersion measures can
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indicate how similar or different in
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terms of variation This
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information is So let's think about an
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example comparing the income of two
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different regions, thinking here in the region
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closest to the coast or
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comparing the income of people who live there
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closest to the Border So how do
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we understand this income of both
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regions The standard deviation can help
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us in this process, it can determine in
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which region the income is more consistent
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or the income varies But we can also
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use this personally for
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risk and investment analysis, perhaps there is an
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enthusiast in the financial market area, right?
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dealing with this
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part, so it is a very
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important tool, the measure of dispersion,
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especially the standard deviation, they are
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crucial to assess the risk associated
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with the investment, so an
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investment that you are analyzing
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that has a high dispersion may be more
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risky may have a greater chance of
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return variation So there are some
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features in addition to what you
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saw in the discipline that
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dispersion measures can help you so see
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how interesting this
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part is let's see here some examples
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some are there in your book so
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let's recap and there are others there that I
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brought new ones first, so let's think
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about a situation where we have three
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students, student a b or c, right, Maria,
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José and Joãozinho who took a
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test
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And these Here were the grades they
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got, student a got the grade 7 student B
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also had a grade s the student had
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a grade of seven if we take the
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arithmetic mean of the three students it will be equal
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to s so the grades of these students are not dispersed
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so they are
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concentrated here in the average 7 so they
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are not dispersed they coincide with the so-called
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ethical arithmetic mean, now let's also think about the
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situation here, you know, of the other three students,
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student e d and f who take this
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same test, so now they are students
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from the same class who took the same
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test, but now we are looking at these
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other separate grades, student D had
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a grade of 3.5 the student and 7.5 and student F
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had a grade of 10 what is the
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arithmetic mean of the students so it will also
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be equal to seven But if we look at it in the
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same way we will
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look at the What is it that the average of these students
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are dispersed in relation to the average,
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only one student got the maximum grade
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close to the Average, sorry, it is equal to
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seven, the other students were
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dispersed in relation to the average of that
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subject, why? Because the average is seven,
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then if we observe student D, he
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has an average lower than seven and
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student F has a grade higher than seven,
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who received the maximum grade, so we are
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dispersed in relation to that average
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S, so by analyzing these two situations
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we will understand what the first
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situation has a much more
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representative result because Because it is more
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homogeneous we can understand that
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the majority of those scores or in the case of
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that specific case all the scores
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are seven when compared to the second
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situation
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in which the average is heterogeneous in
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other words, it is a little more dispersed in
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relation to the average, they are not as
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concentrated close to the average S that was
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calculated
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previously. The
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average deviation, which is the average deviation, right,
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folks, is the sum of all the differences
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in the absolute value of each one of the
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values ​​and the arithmetic mean of all the
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elements analyzed so now we are going to
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take the mean a math test of
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seven students here with
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random grades So if we are going to take the
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calculation of the arithmetic mean we are going to
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add up all the values ​​from that
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set of data and let's divide by the
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amount of data we have
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so let's add them all up 2 + 3 + 5 +
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6 + 7 + 9 + 10 and let's divide everything by
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S by seven because we have scores from
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seven students so the sum of all the
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grades will be 40 42 and we will
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divide by seven so the average will be
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in this case average
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six so now we are going to calculate
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the difference between each grade and the
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average grade which in this case is equal to if and we
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will then for the next step So
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we take what the grade of each of the
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students is and we reduce the value of the Average that
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we found
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previously so the grade of the student
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who got two we take the grade
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minus the average It will result in -4 for the
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other student -3 -1 0 1 3 4 right, these are
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all those grade values ​​minus the
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average that we found
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previously. So let's transform
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all these numbers into positive numbers
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and now we will add up all
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these numbers and the average deviation is the
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average arithmetic of the modules of the seven
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calculated values ​​so again
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we calculate all the results of this of the
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Average minus the grade and we will arrive at the
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value of 16 we continue to have the same
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seven amounts of information So
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let's divide by seven then the
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average deviation of these students considering this
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grade It's going to be
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2.28, so the deviation to get to the
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personal standard deviation, we're going to follow a
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few more steps, right, the
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standard deviation, as I told you, right, it's
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used in several different situations,
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we can look at investments, we can
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look at data consistency, we can
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look at risk So there are several things that
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we will look at and this personal standard deviation
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is defined as the
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absolute value of the square root of the variance
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so that we can get to the root of the variance,
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right, we have some steps to
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follow So let's take the example here
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of calculate the pattern of the values
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found in the table when calculating the
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variance in the previous example, so
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in the previous example we calculated
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the arithmetic mean of the grades, we found
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the variance, right, it was the
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arithmetic mean of the mean
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squared deviations. So we took all those
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average deviation values ​​in addition to the
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arithmetic mean and we square it and with
00:15:39
that we arrive at the standard deviation which will
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be the square root of the variance which is
00:15:48
7.42 let's see another personal example
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now thinking about the standard deviation that
00:15:54
we want to calculate In relation to the
00:15:56
music album, I think everyone here
00:15:58
has heard music, they like listening to music.
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So I think it will be a very
00:16:03
interesting example, let's think here we
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have a music album where each
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song has its own running time and
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In this album we have five songs,
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how are we going to do this? First
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we have to convert all of this to the
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same format, that is, we are going to transform
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this, all these minutes into
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seconds, so all the seconds there that
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we
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have Adding them all up, right the first one
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music there on machine part two guys
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have the two calculate the
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average if we transform the song one that
00:16:39
is 3 minutes and 45 seconds it will have
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what 225 seconds the Second song
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250 seconds the third song 200
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seconds the fourth song 300 seconds and
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the fifth song
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235
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seconds So if we add up all
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these results of seconds for each of the
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songs on the music album and
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divide by five because we have
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five five songs on the album we will
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have an average of 242 seconds more or
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less right there so the average of seconds
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of all the songs on the album are
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242
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seconds so now we are going to
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calculate the personal variance we
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found the average remember in the first
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calculation we found the average which was the
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average 242 seconds So we are going to take
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those seconds from each of the albums
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that we had 3 minutes and a few
00:17:46
seconds and we transformed everything to
00:17:48
second we will take this value minus
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the average the result we will
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square and this we will do for
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each of the songs on the album So the
00:17:59
first song had 225 seconds and the
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average of the songs on the album was 242
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seconds and this the result of this is
00:18:08
squared so having all
00:18:11
these steps here we will arrive at the
00:18:15
total value, right the total sum of all
00:18:18
these values ​​so 289 + 64
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1764 + 3364 + 49 so we have a
00:18:30
total of
00:18:33
5530 so considering that the
00:18:36
standard deviation is the square root of the variance in
00:18:40
absolute values ​​we will divide the sum of the
00:18:45
squared Differences by the number of
00:18:48
songs here there is no mention1 okay guys
00:18:50
to get the variance So we will
00:18:53
take
00:18:55
5530 let's divide by 5 we will have
00:18:59
1106 seconds and it is from this value that
00:19:03
we will do the square root so the
00:19:05
square root of 1106 seconds will be
00:19:11
33.25 seconds So this here is the
00:19:14
personal standard deviation in that album of
00:19:17
five songs that we You can imagine
00:19:20
that it's a rock album, a
00:19:22
samba MPB album, right, the musical style that
00:19:27
you like the most.
00:19:30
We also have asymmetry measures there,
00:19:33
so how are we going to
00:19:36
use these asymmetry measures
00:19:39
in addition to what you're seeing? There in
00:19:42
your course material is a measure of
00:19:46
positive asymmetry, it will tell us
00:19:49
that we have a longer tail to the
00:19:51
right of the graph, which means that
00:19:54
there are higher values ​​than the
00:19:57
average, we will see
00:20:00
these graphs a little better one
00:20:02
negative asymmetry measure will indicate a
00:20:05
longer tail to the left of the graph
00:20:08
with values ​​smaller than the average
00:20:12
of those values ​​there that we from that
00:20:14
set of data that we are observing,
00:20:17
how can we use this in
00:20:19
financial analysis also because if
00:20:22
we look Using a set of data,
00:20:24
we put this in a
00:20:27
graphical representation, we will be able to understand the
00:20:30
distribution of returns on
00:20:32
investments, investments that will have
00:20:35
a positive symmetry are more
00:20:38
likely to have higher returns
00:20:40
since they have
00:20:42
higher values ​​than the average there on the right part
00:20:46
of the
00:20:48
graph but they can also have
00:20:51
long tails with extreme losses and a
00:20:54
negative symmetry indicates that returns
00:20:57
can have a distribution with more
00:20:59
losses than gains. So if we
00:21:02
put all this information there on
00:21:04
that graph we can have a
00:21:07
visualization little better on
00:21:11
financial aspects and here folks we have
00:21:13
the graphical representation of each
00:21:16
of these elements that I mentioned, a
00:21:18
symmetrical distribution will be one in
00:21:21
which the median, the mean and the mode are all the
00:21:26
same if we look at a
00:21:30
symmetrical distribution to the right or positive As I
00:21:33
mentioned to you, we will have the mean
00:21:37
greater than the median and greater than the
00:21:41
mode. If we look at an
00:21:45
asymmetric distribution to the left, we
00:21:49
will have an average lower than the
00:21:52
median and lower than the mode. So this
00:21:56
set of graphs Here it's just
00:21:58
important for us to understand various
00:22:00
aspects, whether it's your course, your
00:22:04
day-to-day life, or something
00:22:06
you want to do beyond college
00:22:09
that will give you several possibilities for
00:22:16
personal interpretation.
00:22:34
Regarding
00:22:37
personal kurtosis, we also have this
00:22:40
graphical representation, right? We have
00:22:42
tails of a distribution that are
00:22:44
different from the normal distribution.
00:22:57
Look at a
00:23:01
graph, right, what will represent
00:23:04
that set of data that
00:23:06
we are analyzing, we can
00:23:09
understand more or less how
00:23:11
that
00:23:13
data behaves, so kurtosis
00:23:16
aims to facilitate the understanding of the
00:23:18
general characteristics of the distribution of
00:23:21
the data under
00:23:22
analysis indicates the degree of flattening or
00:23:25
tapering of a frequency distribution
00:23:29
or Considering the stereogram of the
00:23:31
question in question, sorry, when
00:23:35
we have a kurtosis equal to zero, we
00:23:37
will have the data uniformly
00:23:41
distributed, so there is a very
00:23:44
nice curve there that goes up and down having
00:23:49
the same parameters, which is different from
00:23:52
what we observe here in a
00:23:55
positive kurtosis that occurs, you know, a
00:23:59
heavier tail distribution as you are
00:24:01
seeing here in relation to a
00:24:03
normal distribution, so we see that this is the
00:24:07
solid blue line that the We
00:24:09
previously observed that this
00:24:11
normal distribution represents the positive kurtosis,
00:24:16
it is dotted, right? So it will indicate a
00:24:19
positive value for the short ones.
00:24:28
are
00:24:33
higher and the negative kurtosis we will
00:24:36
have a different graph than the other
00:24:40
two obviously, right class
00:24:43
negative kurtosis it will occur in a
00:24:45
distribution with lighter tails in
00:24:48
relation to a normal distribution So
00:24:51
this dotted line again we
00:24:54
will have it more concave, right, we're going to have
00:24:58
it with a
00:25:01
very uniform distribution too, but with
00:25:04
negative values ​​for kurtosis and it has a
00:25:07
representation that's very different from
00:25:11
kurtosis there, equal to
00:25:15
zero, so when are we going
00:25:17
to use kurtosis, right guys, again
00:25:20
bringing examples in addition to what you
00:25:22
're seeing In your material,
00:25:25
risk and insurance analysis, we
00:25:28
will use it to understand the
00:25:30
probability of extreme events.
00:25:33
When we are looking at some risk or
00:25:35
even some insurance, a high kurtosis
00:25:39
can indicate a greater risk for
00:25:41
unexpected or extreme events in a
00:25:45
portfolio of investment or in an
00:25:47
insurance context So it can
00:25:49
indicate that there may be more
00:25:52
extreme events there, precisely, right? Because of
00:25:54
that little tip that we have up there,
00:25:56
this can also be applied in
00:25:59
biology and medicine studies, just getting away
00:26:02
from what we see in the
00:26:03
discipline, then out of nowhere,
00:26:05
examples of biology and medicine appeared here,
00:26:07
so when we are talking about
00:26:09
medical biological studies, it can help to
00:26:12
understand the biological
00:26:15
or biometric characteristics and Studies, right, of height,
00:26:19
weight or blood pressure, can this
00:26:22
kurtosis indicate if there is a
00:26:24
common concentration of values ​​close to the average, right,
00:26:27
so let's
00:26:28
analyze a set of
00:26:31
information again and understand whether that
00:26:34
blood pressure or weight or height, right, will have
00:26:37
some common concentration in some type
00:26:39
of age population or in that
00:26:42
little piece of data that is being
00:26:46
shown. and last but not
00:26:49
least we have the
00:26:51
arithmetic mean. So the averages, the grades, you know,
00:26:55
in mathematics again, going back to
00:26:58
our great example
00:27:00
of grades in
00:27:02
mathematics, we can calculate the
00:27:05
arithmetic mean of the grades from two
00:27:08
partial assessments, right, so we
00:27:10
can calculate the value of the grades P1 and
00:27:14
P2 and we can divide
00:27:17
these
00:27:18
values ​​by two. So if we use
00:27:21
two values, what will we do?
00:27:23
Take those two values, add them and divide
00:27:25
by two. This will be the arithmetic mean
00:27:29
represented here in this formula,
00:27:31
right, which is o o a plus b divided by 2
00:27:36
if we use an arithmetic mean
00:27:38
of three numbers we will add the
00:27:40
values ​​of a b c divide by three because
00:27:44
there are three different values ​​that we
00:27:46
are looking at but we can also
00:27:49
look personally this for an
00:27:52
arithmetic mean of n numbers of several
00:27:54
numbers So we will have what the
00:27:57
formula a b + c plus z divided by
00:28:03
by n which will then give us the formula
00:28:05
to understand the arithmetic mean in a
00:28:08
large set of data Of course we
00:28:11
have Excel's help, right, Excel helps
00:28:14
everyone a lot, but it's important that
00:28:16
we know what's behind Excel, right? So how is
00:28:18
Excel calculating
00:28:20
that arithmetic mean? How is Excel
00:28:23
calculating the standard deviation, right? So it's
00:28:25
important that We know this, but
00:28:27
Excel is there, so we know that it
00:28:29
also helps us with these
00:28:33
calculations. And we also have the famous
00:28:37
arithmetic mean, weighted or just the
00:28:41
weighted mean, so for us to
00:28:44
calculate the weighted mean, it's a
00:28:47
little different. The idea is the same
00:28:49
but we have some different steps
00:28:51
to follow So let's think about
00:28:54
calculating the
00:28:55
arithmetic mean of this quantity here
00:28:59
of
00:29:00
elements that are being shown here
00:29:03
in the second line we have some
00:29:05
quantities of 3 4 5 6 and 7 So how
00:29:10
do we do this, right? We are going to count
00:29:14
the number of times each number
00:29:17
appears, three will appear four times
00:29:20
in this data set, four appears
00:29:22
twice, five appears once, six
00:29:25
appears five, seven appears three times,
00:29:28
so the weighted average or
00:29:31
arithmetic mean weighted is obtained
00:29:33
more quickly when we calculate the
00:29:35
sum of the products of each number
00:29:39
multiplied by the number of times
00:29:41
it is repeated then divided by the total number
00:29:44
of numbers
00:29:47
considered. So we will take these
00:29:50
values
00:29:51
and arrive at the result of 76
00:29:57
divided
00:30:00
by 15 which will be
00:30:04
5.06
00:30:06
guys so that being said,
00:30:08
these here guys are the contents
00:30:12
that we managed to bring to
00:30:15
you today, right, they are just some, as
00:30:18
you may have seen that we have
00:30:22
several in our material,
00:30:25
but but we We can't address
00:30:28
everyone, right, we have limited time and we
00:30:31
will now have an
00:30:35
interactive connection and I left the invitation here
00:30:38
for you guys, I left the
00:30:41
QR code here for each of you if
00:30:44
you want to watch and I'll share the
00:30:47
access link Also here in the
00:30:51
chat let me get the link
00:30:59
and here is the personal link so
00:31:02
you can watch the
00:31:05
interactive connection that today will be about
00:31:08
Maker culture and
00:31:11
[Music]
00:31:12
society Oh I see there are some questions
00:31:16
about the test, right the teacher kess
00:31:18
is helping us,
00:31:29
beauty guys, I sent it here in the chat and
00:31:31
I will send it here again the link to the
00:31:33
interactive connection that we will already
00:31:37
have, which is Maker culture and society,
00:31:41
Professor Kess answered the questions about
00:31:46
the test, right?
00:31:49
to answer
00:32:12
just a second,
00:32:31
guys, in the world, the teacher k is helping
00:32:34
you answer the questions, right about
00:32:37
the
00:32:38
test, so I would like to thank
00:32:40
all of you for participating and my name,
00:32:44
right, is the tutor teacher Cassiana, the
00:32:46
tutor teacher Felipe, the
00:32:48
tutor teacher kess who is helping us here,
00:32:50
thank you very much, kess, tutor
00:32:53
Lis and Luana,
00:33:01
I will also go back to the previous slide
00:33:04
so that you
00:33:06
can project here if you want to access it on your
00:33:09
cell phone QR Code You don't have the
00:33:12
interactive connection link here in the chat, which
00:33:15
you can also
00:33:17
access The recording will be made available
00:33:20
to you and soon it will also be
00:33:23
available in the week's materials.
00:33:31
This has already started, right, it's already
00:33:35
19:34,
00:33:36
the Live, right,
00:33:47
interactive connection, beauty guys, so good
00:33:50
evening
00:33:51
everyone, thank you very much for
00:33:54
your presence, if you have any questions, right, you can go there
00:33:58
Don't talk to us, I'll be
00:33:59
answering this for you Oh, Professor
00:34:03
Kess shared here that everyone
00:34:05
will receive instructions in the notices, right,
00:34:10
instructions will be made available closer to the test.
00:34:13
So it will help you a lot to clear up
00:34:16
any doubts that may still
00:34:20
arise Good evening
00:34:24
Guys, thank you very much,
00:34:26
Antônio, being with us
00:34:29
today, have a good weekend for you, have a
00:34:32
good weekend,
00:34:39
everyone, this is on the 15th, can you talk?
00:34:45
Thank you, have a good night, have a good
00:34:47
weekend, too, may
00:34:49
God bless you, can you continue? I'm here, you can
00:34:52
continue talking, I'm here Great,
00:34:54
thank you
00:34:55
Antônio, we also have the
00:34:58
interactive connection, you will see the module evaluations,
00:35:00
which you will soon
00:35:03
receive, right? Some information, the
00:35:19
most perfect, Professor Kess asked
00:35:22
to reinforce and we will reinforce again on the
00:35:25
15th/ 04 we will have the interactive connection
00:35:30
to the summer module evaluations
00:35:33
so you will receive this link,
00:35:39
the information with the time access link will be available in various ways
00:35:41
so it is important that you
00:35:44
watch this interactive connection because
00:35:46
I'm sure that In addition to the notices that
00:35:48
we will send to you in the
00:35:51
disciplines, it is still important that you are
00:35:53
part of the interactive connection to resolve
00:35:55
other doubts that may
00:35:57
arise and everything else with all
00:36:12
possible guidance, that's right, all doubts
00:36:15
are answered regarding
00:36:24
personal assessments. A big hug to everyone, thank you very much
00:36:28
and see you guys

Description:

TIPO Profa.-Tutora: Disciplina: Tema: Data: 00/00/0000

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