Statistika (4) - Rata-rata - Mean, Rumus Rata-Rata - Matematika SMP

Hello friends, see you again with me on the legolas channel. In this video we will continue our study about statistics. We will learn about the range, we will also learn about the average or mean. Don't forget for friends who haven't subscribed, subscribe to the legolas channel so you can get the latest updates from my videos.

Let's just start, the range is the range of a data set. Range means we want to know how big the distance between the smallest data to the largest data. So the formula is very easy, the formula of range is x or the largest data minus x or the smallest data. So the largest data is reduced by the smallest data. Meanwhile, the average we want to know,

How much is the average? Or if we equate all the values With the amount of data, how much is the range? Average or

The formula is the number of data values divided by the number of data. Later, if we are here, we will learn for single data. We don't learn for group data. Later, if the group data is learned in high school, if it's in high school, we learn about single data.

Now let's go straight to the example of the question, so from the following data there are numbers 8, 7, 7, 5, 8, 10, 9, 8, 7, 6, 5, 4, 2, 6, and 7, we are asked to determine the range of the data, also the average. Okay, let's just go straight, if the range or range

This is really easy, we just need to subtract the maximum x with the minimum x. We just need to look at the data here, what is the largest data? Oh, the largest is 10. What is the smallest? The smallest is 2. Well, that means we only have 10 subtracted by 2, so the range is 8.

How about the average? Well, the average is easy. The average formula, I have explained earlier, the number of data values. What does the number of data values mean? Well, we sum the data. 8 + 7 + 7 + 5 + 8 + 10 + 9 + 8 + 7 + 6 + 5 + 4

plus, this is the number you add, plus 2 plus 6 plus 7 divided by the number of data, if this is the value we sum up, how much data we sum up, if this is how much data we calculate, there are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, later divided by 15.

We will sum up, it's not difficult to calculate the questions, just train us to calculate carefully. We will try to sum up, 8 + 7 = 15, 15 + 7 = 22, 22 + 5 = 27, + 8 = 35, 35 + 10 = 45, 45 + 9 = 54,

54 + 8 = 62 62 + 7 = 69 69 + 6 = 75 75 + 5 = 80 80 + 4 = 84 84 + 2 = 86 86 + 6 =

92 + 7 = 99 oh, it turns out that if we sum up all of these values, it will be 99 divided by the number of data, which is 15

We can simplify this, right? Don't divide it, if it's already SMP, don't directly divide 99 by 15, okay? But if you prefer, we can divide it. We divide it by 3, the result is 5, 15 divided by 3. 99 divided by 3, the result is 33. So 33 divided by 5, this is 6, 3 divided by 5, or 6.6. This is the average of question number 1.

Let's try again, zone number 2. Well, this is actually the same, only the data is more now. We have a height of body, that's it. From the data above, we are asked to determine the range. If the range is that, it means range. We are asked to determine the range. What is the range? We look for the largest data. The largest data is 128, 127, is there more than 128? There is none, so the largest data is 128.

then 128 maximum, minus the smallest minimum 100 and below 110 we see there is no, means 110 so the range is 18 easy huh now we are told to determine the average

On average, we will sum all the numbers. 128 plus 127 plus 127 plus the last 128 divided by the number of data. Let's try to calculate how much data there is.

There are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. Wow, our number is 20. The value itself, if we sum it up, I'll help you calculate it later. If we sum it up, it's 2414 divided by 20.

We just divide it. This means 2414, we divide 2 first. We divide 2, 1207. 1207 divided by 10, then the average height of the body is 120.7. So it's not difficult. But it's still difficult to calculate. This is if the single data is in the form like this. So the data is just normal.

Now we want to try how if the data is in the form of a table like this. The table can be like this, the table can also be heavy, there is a frequency. If this is the right table, the table can go down. The weight is 32, the frequency is 3.

34 is equal to 6 35 is equal to 14 we have to remember that frequency is the number of the data so if 34 is equal to 6 35 is equal to 14 so there are 14 children with weight 35 let me write it down first this is 17 38 8 40

If the data is in this form, then the easiest way is to make another table or column. Or if we make another row like this, that is the weight or value multiplied by the frequency.

Why? Because we will need this to find the average. In this question, the range and the average are asked. If the range is very easy. If the range is 40 - 32, the result is 8. The largest data minus the smallest data.

But if it's even, it's impossible to calculate like this. So if it's even, it's impossible to calculate 32 + 32 + 32. There are 3, sir, the data. Then, + 34 + 34 + 34 + 34 + 4 + 5, eh 6. Impossible. Why? We'll be drunk at 35. So if we find a question like this, we just multiply it first.

32 x 3 = 96 34 x 6 = 206 35 x 14 = 490 37 x 17 = 629

38 multiplied by 8, 304. This time the result is 80. So we get this from this multiplied by this. Now, this is very easy. So when we find the average,

What we sum is not the data itself, but what we sum is this 92 + 206 + 490 + 629 + 304 + 80 divided by the number of data. Now we must sum the number of data. Where did we get the number of data, bro? Let's just sum the frequency.

3 + 6 + 14 + 17 + 8 + 2 How much is the result? 8 + 10 + 20 3 + 17 + 20 + 20 + 20 + 10 Oh, the data is 50, bro. 50, the data is 50.

Now we just add up 92 + 206 = 298 298 + 409 = 788 788 + 629 = 1417 1417 + 304 = 1721

1721 + 80 = 1801 But you are wrong here, it should be 96 + 4 again, so it should be 1805 Now we have 1805 divided by 50, we divide 5, 1805 divided by 5 3, 15, this means 36

This means 1. 361 divided by 10. Because I only divide by 5. The result is 36.1. It turns out that the average weight of the body is 36.1. So if you find the table, don't count them one by one like this. This is wrong. It's not wrong, but it's wasting time. So we multiply it first.

the value and the frequency we sum up then we sum up the frequency, the average is divided by the value divided by the data number now we have the following example of the question if the previous one, these three are examples of finding the average it's actually not difficult because you can definitely do it when you were in sixth grade you also studied it just need to calculate it carefully

Now this one, this one is reversed, if this one we are a little bit reversed because we know the averages. If you meet issues like this, for example, usually he asks the last test value, like this, what is the fifth test value to get a certain average value.

Well, let's assume we're looking for the average. So don't be confused if you don't like memorizing formulas. So we don't need to memorize the formula for the fifth test, which is equal to how many divided by how many. It's hard. What we memorize is the average formula. The average formula is the number of values divided by the number of data. What does it mean, sir? Memorize this and then you can work on this issue. Let's read the question.

Johan got the test values of 70, 60, 100, and 95. These are all values. The values, the values, the values. Determine the fifth test value. There is the fifth test value. Oh, it turns out the value is like this. There are 70, there are 60, there are 100, there are 95, there is the value of X. We don't know the fifth value yet. The average is 80. Oh, this is the average.

So we just have to put it in here, 80 is the average that we want. The number of values is 70 + 60 + 100 + 95 + the last repeated value if divided by 5, we want 80.

Now we want to find the x. How? We move the 5 here. Multiply by 1. This is 80/1. Multiply 1 here, no problem.

So it becomes 80 multiplied by 5, 400, equals to, we will add this, 130. 130 plus 100, 230. 230 plus 95, means 325. 325 plus x, because we don't know the x yet.

If it's like this, it's really easy. It turns out that X is 400 minus 325 equals 75. So what we memorize is just the average formula. Let's try the fifth question. Here the average value of 48 students is 6. If the value is added from 2 people, the average becomes 6.1. Determine the average value of those 2 people.

The same principle that we memorize is the formula for the average or the mean is the number of values divided by the number of data. The value is divided by the data. But in question number 4, the math is only 5.

If here, the average of 48 students is 6. Actually, we can assume that there are 6 48 pieces. 6 to 48 pieces. But if we sum it up like this, it's complicated. If we meet a problem like this, which has a lot of data, we make a simple table. We have values, we have frequencies.

Let's assume the value is 6 and the frequency is 48. Then we have another value that we don't know yet. The average value of two people is this. Determine the average value of those two people. We don't know the average value of those people. We don't know the average. One can get 9, one can get 7, the average is 8. We don't know.

But what we're looking for here is the average of those two people. The frequency is only two people. How about we multiply this? This is the value multiplied by the frequency, 6 multiplied by 48, this is 288, then x multiplied by 2 is 2x.

while the frequency number, if we sum it up, the number of the frequency is 50. How to find the average? Find the average, the number of values, 288 + 2x divided by the frequency, 50.

What is the average? 6.1 So this is multiplied by the sine wave, right? That's right, multiplied by the sine wave 6.1 multiplied by 50 The result is 305 equals 288 plus 2x So we get this

305 - 288 = 2x This is 17 = 2x So the x is 8.5

So, the average of those two people is 8.5. What's the value? It can be 1, 9, 8. The average of those two people is 8.5. So, if the question is like this, it's a bit long, we make a table. Let's try again. For example, the average of 15 numbers is 11.4. So, there are 15 numbers, we assume the value is 11.4.

The average of 8 numbers is 12.5. Oh, we divide it. There are 15 numbers. The first, second, third, and eighth numbers are 12.5.

The next 6 numbers, the next 6 numbers mean from 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6. This one, the average is 10.5. There are 15 numbers that we don't know, we are told to determine the 15th number.

So it's actually the same, we can make a table, we have a value, I'll try to make the table a little bit down, we have a frequency, later we will definitely need a value, we multiply it by the frequency, the value is 12.5 with a frequency of 8 numbers.

The second value is 10.5 with a 6-digit frequency. We multiply 12.5 by 8 is 100. This times this is the same as 100. 10.5 times 6 is 63.

we have the 15th number, this is a different color, the 15th number is x, this is x, the 15th number has only one frequency, and this is x, so if we sum it up, if we sum up the frequency number, it's 15, it's 15 numbers, the number of the value is 100 + 63 + x,

163 + X. Now, what we remember is the formula for the average. The formula for the average is the number of values divided by the number of data. The average that is obtained, well, the number of values, if we look for the average number, the number of values is 163 + X divided by the number of data, 15.

turns out to get the average of 11.4 yes, we multiply this by the cross 114 multiplied by 15 027 this means 570 then this is 114 yes 114 times 5 570 114 times 1 114 we just have to multiply 10

1710 but there is a comma, so comma 1, so 171 = 163 + X, we get now, the X is 171 - 163, the result is 8

Got it, the number is 8. So, that's it. For the range, it's the easiest. We just need the biggest x, minus the smallest x. For the number 1, 2, and 3, we're looking for the usual averages. Number 4, 5, and 6, it's a bit reversed. But what we remember is the average number. Because we want to find the average too, actually, in that question. If the number is a bit too much, we can make a table.

Thank you for watching this video. Good luck. If you think this video is useful, share it with your friends so they can learn and get good grades. Don't forget to like this video, subscribe to Legurles channel, and follow his Instagram. Thank you.