MÉDIA, MODA E MEDIANA | MEDIDAS DE TENDÊNCIA CENTRAL \Prof. Gis/

Mean, mode and median? Average, you know, right? Arithmetic mean Anyone who has never calculated the arithmetic mean of their grades to see if they passed the year got there at the end of the year, got desperate and went to do this calculation, you already know, right, but now what is mode and mode median, let's take a real context What's fashionable nowadays is what clothes, what sneakers or using what notebook or those toys, the jars are in fashion.

What it means to be fashionable means that it is appearing very frequently. In mathematics, when I say what the mode of the sequence is, a sequence of terms here is the one that appears most frequently, okay, and the median, the median is easy to determine who is the central term of the sequence. So let's go determine the median mode and the arithmetic mean of the elements of the Set 8 9 10 7 6 5 and 6.

Let's pretend then, since our exercise is not contextualized that here I have the grades of the students in a classroom , you can be a small room there that I had pretend people. So first let's calculate who the fashion is, it's easy, right, fashion, so just look at the sequence and check the one that appears the most times. Which one have you already seen or do I need to put it in the sequence so you can see it?

So let's start the exercise, not necessarily necessary, but let's put the terms in the sequence that we call Rol, Rol means putting the terms in an ascending or descending order, I'm going to put the lowest in ascending order, so the lowest score here was 5 who Did people get a 5 on the math test, right? Then I have a 6 and another 6, 6 and 6, then there's a 7 and then there's an 8. There's someone who attended Gis's class who got a 9 and someone else who also watched Gis's class, who got a 10, kidding people, well, now it's easy, it was already easy to see who was in fashion, right?

So fashion will be the term that appears the most. So it's going to be 6 because it appeared twice here in the sequence, so the mode is the number 6, okay now people happen to have cases, pretend if I put another 10 here who would be the modes would be the number 6 and the number 10 then we would have two modes and then see here we would have one called bimodal when it has two notes it is bimodal if there is no number that is repeated more times it would then be amodal when there is no mode and if a sequence appears, for example it would be 6 or 10 and 8 here the terms that were appearing several times then we would have multimodal. Okay , so brand bimodal multimodal and amodal fashion, okay?

So continuing, who will be the median, median is the central term of the sequence as here I have let me see one two three four five six seven I have an odd number of terms it will be easy to find I did it like this, right when I calculated I I eliminated one from here with one from here, one from here with one from here, one from here with one from here, whoever was left in the middle there alone, so it's 7, so it's the median, this is easy because I have an odd number of terms, I'll explain when it's a quantity par is fine and lastly we need to calculate who the arithmetic mean is, remembering that here we have simple ones , right? I want to know what the arithmetic average of the math grades of the students in my classes was, I'm going to add all 5, 6 plus 6 plus 7 plus 8 plus 9 and 10 and I'm going to divide all of this by 7 because I have seven grades here so Then I will find the result of the arithmetic mean. Who is good at mental calculation so we can do this mentally or are you ok, so come on, help me 5 plus 6= 11, 11 plus 6= 17 plus 7= 24 plus 8= 32 plus 9= 41 plus 10= 51, did it there too, if you didn't do it in your mind, you did it on paper and it worked too, if you don't correct Gis, look, 51 / 7 now I come here and do the division 51 by 7, you're an ace at division too, so let's go 51 by 7, that's seven times, 7 x 7= 49 left here 49 to 51 I'll have to borrow from 20, then it's 20, 20 / 7 are two times 2 x 7= 14 left 6 doing it straight here I add another 0 there are 8, 8 x 7 = 56, there are 4 left , well, two decimal places are good, right people, because I see that here we only had whole numbers.

So this means that the arithmetic mean will be 7. 28. And then if we want to round to one decimal place if you want 7.

28 I'm going to round this two, so I look at the neighbor's neighbor, it's 8 went from five so I round this to 7. 3 because then this 2 will go up to 3, okay if I wanted to do it but I I could leave 7. 28 because when we work with a decimal place, perhaps the interpretation will be clearer, right?

7, generally 7 is the average in most schools and in your school the average is up to 100, which is what you can tell Gis in the comments. And now we are also going to calculate the mode, mean and median when we have an even number of terms, shall we? If you don't understand very well, go back to the classes where I explained mean, median mode, everything separately with contextualized exercises, all the links are in the description, okay, then you understand, you can do all the activities, here I have it, determine the median mode is the arithmetic mean of the elements of the Set 12 11 15 14 11 and 16 that we will here pretend that here are the ages of the students in the gis room, let's pretend that this is the age of the students, so to calculate the median we will put this sequence here in Rol, remembering that in Rol it is in ascending order so it will start here I think there are 11 and 11 two 11 then 12, 12 then comes 14 o14 then we have 15 and 16.

Okay then I put it the elements in ascending order now so to calculate let's start with the mode like we did in the other one, the mode mode is the one that appears most in the sequence, which is 11 because it appeared here twice, right is its frequency, 11 is the mode, who is the median Me median is the central term remember how I did it I eliminate one from there with one from here, one from there with one from here, hey now see there are two left there are two left here two central ones how do I do the calculating the median when we have two centers? You simply do the arithmetic mean of the central terms so here I'm going to do 12 plus 14 and divide by 2 because I'm doing the arithmetic mean to find the median which here has two terms 12 plus 14 of 26 and 26 / 2 = 13 so I mean that the median of this set of elements is 13, okay, and now we're missing the arithmetic mean, which I 'm going to represent by Ma, we're going to take all the elements in the order they are there, right? 11 + 11 + 12 + 14 + 15 + 16 all of this I must divide by one two three four five six which are six elements in total people so it is like this if the number of elements is odd an odd quantity will always have the central term to calculate the median if that quantity was always an even quantity you will have two central ones and then you must calculate their arithmetic mean, okay, mark it well then, let's go arithmetic mean here, 11 + 11= 22 with 12= 34, 44, 48 with 15= 58, 63 , 79 look there, I'm good at counting in my head so I should divide 79 by 6 and then we'll divide where here, there's no space, guys, I'm going to do it here in the corner 79 by 6 you can see it well there 79 by 6 will be one times six from six there are 1 left, below 19, 19 by six are 3, 3 x 6 from 18 there are 1 left, I add the comma and a 0 then it will be 1 x 6= 6, 4 left and if I continued this calculation, putting a 0 would give 6, 36 there would be 4 left and it would end up being a decimal and then we always work with rounding, right, it would be 13.

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​​So try rounding this one here, look, I'll look at the neighbor, the neighbor went from 5, so that one will become 2 when rounded, okay? This means that my arithmetic mean here will be 13. 2, I said the age of the students is 13.

2 years old, you can do an arithmetic mean, median and mode guys, I hope you understood Gis's class, you liked the explanation if you didn't understand very well, go back to the contextualized classes about this content, there are three different classes, okay, then you can clear up all your doubts, leave a super like for Gis, subscribe to the channel and I'll see you in the next class, bye. . .