Statistika (6) - Modus, Tabel Distribusi Frekuensi, Rumus Modus - Matematika SMP

Hello friends, see you again with me on the Legur Less channel. In this video, I will continue our study of statistics. We will learn what is called a module and I will also teach you a little about how to make frequency distribution tables.

Modus is the most data in a data set. This modus can be more than one. The way to find it is very easy. No formula, no anything. Just see the number of the most numbers. The frequency distribution table means like this.

If we usually look at the data table, it is usually a single data displayed in the form of a table. For example, this is a single data displayed in the form of a table, where the number 32 is 3, the number 34 is 6.

But the data can also be displayed with a certain range of data. To make it, a wide interval is required. The question can be known or searched with steps like this. Here we can see if the data is in the form of a range.

We don't know the exact data, the facts, or the value. So we only have information that between 21 and 25 in this class, we call it a class, there are two data. Can it be 21 and 22? Yes, it can be 22 and 23.

It can be 23 and 24, it can be 22 and 24, it can vary. We don't care, the number must be 2. Well, the class width can be seen from here. So here we have what we call the bottom edge, we have the top edge,

We just need to subtract this, not 25 - 21 but 26 - 21, that is the interval of the class. "What is this, sir?" Log, this is actually a logarithm. Usually in the question, it is told, for example, log 50 is this much.

Then, we can also be told that log 37 is this. Usually, this is the data. In high school, we are told that the data is 50. We are told that the log 50 is this. The data is 37. We are told that the log 37 is this. In high school, it's different. We can use an calculator. Of course, the result is not round.

Usually we round it up. This can also be not round. Usually we round it to the odd number. Why is it to the odd number? Because this is very helpful later if we look for the average mean. But we don't learn here. What is the range? Don't forget this is range. This is only the smallest data. Big data, maximum data.

minus the smallest one. Now let's try it. This is an easy example. We are told to determine the modus, we are told to see this data. We just have to see, for example, number 1, we just have to see who has the most data. This 8, no, 2 is definitely not possible. 2 is just alone. 4 is just alone, not possible. 5 is also just alone, not possible.

6, 6 has 2, 6 has 2, 1, 2 7 has 1, 2, 3, 4, oh 7 has 4, 7 has 4 so we can sort the data, so finding the modus is really easy 8 has 1, 2, 3, here is 3, 8 we can sort, 9 has 1, 11 has 1 so here it looks like, what is the modus? the modus means 7

because it has the most data, there are 4 pieces so it's really easy, let's try it now for this one, we just have to see this 100, let's try to delete it first or we can also list it, so if we list it, we will see how much data is there, we list it, we have 110, only 1 then we have 112

then we have 113, there is no 114, only 1 115, there is 1 116, there is 1, 2 116 117, there is 1, 117 116, there are 2, there is 1 117, there is 1 118, there is only 1 119, there is only 1 116 120

Oh, there are two 114s. Ah, it's past one. So, this is the use of us sorting, so it's visible. Is there only one 122? There is no 123, there is only 124. There are two 125s. There is only one 126. There is one 127, there is one, two, three, four. There are four 127s. There is only one 128. From here it is very clear. Who is the modus? Well, this is the modus.

which is 4, which means the modus is 127. Now let's try if the example is like this, it's so much easier. So if we meet a single data table, we are told to determine the data mode above, we just need to see the frequency. Whose is the highest frequency? This is the highest. Yes, that means the modus, there are two, the modus is 35.

and 37. Let's try number 4. This is the data of the mathematical value in class 7A, Ijuk School of Performance. Determine the modus, find the largest number, the frequency. Oh 19. So the modus is 7. The number 7 is the value, not the 19, but the value of the data.

Well, that's how easy it is. So the modus is actually very easy to find. So compared to the mean, average or median, this is the easiest. So it must be the most answerable if we meet the repetition issue. Now we will learn about the frequency distribution table, how to make it. We already have the steps, but for this question, it turns out

We have been told the width of the class interval, 8. The width of the class interval is 8. Let's see first, the smallest data, what is the maximum? Then what is the minimum data? This starts from 33, so you have a lot of data like this. It is asked to make a frequency table with a width of the class interval of 8 starting from 33.

The most suspicious is the smallest one. Let's try to find the other one. Is there another one? 36. No. This one. It turns out that if we look at 33, it's the smallest one. This is 33. Then the biggest one is... How much is it? 90? 95? Is there more? 98? 99? Is there another one? 99?

This is like calling the queue number 99, is there? It turns out there is no maximum of 98 So, we can know if the range or data threshold is 98 - 33 this is 65 but here it is not used because we already have the class interval starting from 33

then we make the table we have the class we just need this a little bit because we can't not enter 98 so if later it turns out to be in 97, it means we have to make another class then we have the frequency how to calculate the frequency, we will see later

The class starts from 3, but don't make the next one first. It has an interval of 8. So we add 8 here first. So the result is 41. Then we add 8 again to the bottom, it becomes 49. Add 8 again, so we make it to the boundary. We add this interval to the bottom, not to the side.

49 + 8 = 57 + 8 = 65 + 8 = 73 + 8 = 81 + 8 = 89 + 8 = 97

This should be enough. This means 33 to 40 before this. Easy. This means 48. This means 56. This is 64. This is 72. We see the previous class. This is 80. This means 88. This means 96. This means 96 plus 8. 104.

Then we usually make a line like this so that it doesn't get messy. Then how do you fill in the frequency? How do you fill in the frequency? The way to fill in the frequency is to make it straight. So let's look here, 70, 70 is here, 1, 40, 40 is here.

69 is here, continue 71 is here 65 is here 63 is here I continue first here I have helped to make the sequence it was only until 80 here I have made it, it turns out the result is like this it turns out that between 33 to 40 there are 4 data

In 41-48 there are 2 and so on. So if you tell me it's really easy. For question number 2, you are asked about the class of the modus and the class of the median. So what you are asked is if the distribution table is like this, data, mass, it only asks about the class. Why? Because if you ask who is the modus, who is the median, you will learn it in high school, the formula is RUOT.

The class is the easiest. The class mode is here. This means the class mode. The mode should be between here. Because this is the most, 21. For the median class, we must make the cumulative frequency first. This is 4, 4 + 2 = 6, 6 + 5 = 11, 11 + 11 = 22, 22 + 21 = 43, 43 + 16 = 62,

plus 13757980. It turns out that the data is correct. So to find the data to which there is a median, then we use the formula from the previous video. Then for Q2, because the data is correct, we use the formula 2/4n plus 1/2.

even this is 2/4 times 80 plus half means this is data to 40.5 yes data to 40 and data to 41 means if we look at the classes that exist so this is from 33 to 40 we call it class this means data to

12, this means the data of 12 to 22, this means the data of 23 to 43, which means 40.5 or 40 and 41 are also here. So it turns out that the class of the Modus and the class of the Median are the same. This is the class of the Median. Who is the Median? That will be learned in high school.

Well, that's if we have been told the width of the class interval. What if we haven't been told the width of the class interval? So what we haven't been told here. Then we will use this formula. So we will find the range first.

We are looking for the largest and smallest value first. So we calculate the data first, how much is there? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. There are 10 to the side, there are 1, 2, 3, 4, 5, 6, 7, 8. 1, 2, 3, 4, 5, 6, 7, 8. So in total here we have 80 data. We have 80 data.

we want to find the initial range first so first we look for the range first, yes, it means the smallest data is reduced to the largest data here the smallest if we look at it is C33 I don't see the smallest one then the largest is 97

The largest is 97, which means the range is 97 - 33. This means the result is 64. The gap is 64. Then we look for the number of classes or K. This is 1 + 3.3 * log 80.

So this is 1 plus 3.3. The log of 80 is usually given in the question. Here it is not given, so I will help you calculate. The log of 80 is 1.90. So this is 1 plus 6.27. The result is 7.27. We round it up. The result is 8.

So, the number of classes is 8. Now, we are looking for the third step, which is the interval. The interval is 64 divided by 8. So, the result is 8. Oh, the interval is good.

Now we just need to make the table, so the class can start from the smallest, it can start from the bottom, but not the top. For example, I want to start from 30, so 30 is okay. So this is 1, 2, 3, 4, I make the table a little less,

then we add 8 to the bottom first, 30 + 8 because earlier we got the interval 8 too, so this is 38 + 8 again 46, 54, then 62, then how much is this? 62, then it means 70, 78, then here we have 86, okay?

Then we look here, it means 30 to 37, this is up to 45, this is up to 53, this is up to 61, this means up to 69, this is up to 77, this means up to 85, it means 85 plus 8 is only 93.

it turns out that the data 97 must not be included, it can't be included here so we make another one 94 to 100 then we will start a fairly tedious work we will make it straight 80 means it enters here 92 means it enters here

then 82, I'll enter it first, this is the result, so if we look at classes 33-37 there is only one, in classes 38-45 there are three, and so on

The cumulative frequency is already made here, so 1 + 3 = 4, 4 + 4 = 8, 8 + 4 = 12, and so on. Finally, we get the cumulative frequency of 80. So this is the first problem. The second problem is to determine the median class and the modus class. So it's easy, let's just look at the most, oh this is the modus. So the modus class is

this is the class of the modus, it's in the 78-85 class for the median, we need to find the Q2, because the data is 80 again, we use 2/4 times 80 plus 1/2, we get 40.5

then this is the 40th data and the 41st data if we look here, it should be here because this is the 29th to 43rd data then the median class is 70 to 77

Well, that's the mode and the median. It turns out that you can also ask the mean or the average. How to find the average?

So if you are asked to find the minus from this data, it's actually a bit of a pain in the ass for high school students. But actually, if it's minus, it's still easy. We use the middle value. What is the middle value? The middle value is easy. 37 + 30 divided by 2. 45 + 48 divided by 2. This should be the result if we calculate 37 + 30 = 67 divided by 2.

then we get 33.5. The next thing we get is... So, we need to find the middle value first. If we already get the middle value, then we calculate the middle value multiplied by the frequency. So, 33.5 multiplied by 1. This is 33.5. Then, 41.5 multiplied by 3. The result is...

124.5 and so on, we multiply 49.5 x 4 = 57.5 x 4 and so on if everything has been multiplied, then we just have to multiply it we just have to multiply the number of the value of the data, how much we multiply the result if it is multiplied is 5944 so when we look for the minus, we just have to use the value of the data

divided by the data frequency or the number of data the value of the data is 5944 divided by 80 later the result is 74.3 so the average value of this data is 74.3 but indeed if we calculate directly, add this then we divide 80 maybe the result is close not exactly 74.3

So, that's about it. Actually, for the simple questions, it's very easy. We just need to find the most. So, for the table, if it's already known, it's easy. All we need to remember is starting from 3, 3, then don't add 8 here. So, we add 8 below first.

Now, if we make a table from zero, we look for the range, we look for the many classes, we also look for the intervals.

Well, that's about it. Thank you for watching this video. Hopefully it's useful. Happy learning. If you find the video useful, share it with other friends so they can learn and get good grades. Don't forget to like the video, subscribe to the Legoless channel, and follow Legoless Instagram. Thank you.