00:00 Hello, my name is Oyase Sunday. I'll be taking you mathematics today,

00:19 yes, it's three classes and we have an interesting topic. A topic for today is measure of central

00:25 tendency. You want to have an experience of the mid-media mode, but today we're taking a bit of a

00:32 dimension to each measure of central tendency. Now, what's the objective of the class? The objective

00:40 of the class, number one, is to review those previous works on me, median, and mode, is to review

00:47 the works on those three, the tools of measure of central tendency. Number two is to calculate the

00:53 median of a given set of data. Let's have a data to calculate the median of a given set of data.

01:00 Number three, to find the mode of a given set of data, number four, to calculate the mean

01:07 of any given set of data. Number five, to find the range of any given data. So we're good, the

01:15 application of these two is what the class is designed to be. So let's start off with measure

01:22 of central tendency. The measure of central tendency summarizes a data set by giving a value that

01:29 is close to the center of a data set. It's summarizing the data set and what does it do by giving a

01:39 value that is close to the center of the data. In this chapter, we'll be reviewing the median mode

01:46 and mean. And you also learn about the range, which is another kind of summary statistics that summarizes

01:53 a data set. Now, we compare the data set using the median and the range. So let's pull it off.

02:02 You compare data, you have a set of data, you have your mean, median, mode, and range.

02:10 But the two are most vital in comparison. You have the mean, which sometimes they use as x bar

02:20 and we have the range. Now, so when you look at this carefully, these two are basically used

02:29 forward for comparing what data. Now, move ahead. We'll pick the median. We say the median is the

02:38 middle value of a set of numbers or set of data. When all the values are placed in order of size,

02:47 the middle value or the middle of data in a given set of data, when all the values or all the data

02:56 are placed in order of sizes, that means they are well arranged. So if there are odd number of values,

03:04 there will be the one middle value that is in the numbers that are given are odd. The definitely

03:10 you're going to have what or one. But in the order of the numbers are even, then there will be two

03:17 middle values and the median is taken to be the middle way between the two values. So what does

03:23 simply mean? It simply means that it depends on the data distribution given. If the data distribution

03:30 given is an odd number, now the middle value is expected to be one. What if it is an even number

03:39 we are expecting to have the middle value to be two? And even as a date, you expected to pick the two

03:45 divided by two and still find the mean. Now, we move on to question number one to make it a bit

03:52 simpler. Now, what do we do? Look at the first question, question number one.

03:58 What are we looking at? Question one. Question one says find the median of the following data set.

04:03 You have 11, 5, 6, 5, 9, 7 and 5. Now, looking at this set of data, what should be the first thing?

04:13 There are no well arranged. So you cannot just pick up the middle of this set of data. There is a need

04:18 to rearrange the data in the order of sizes. So now, let's pick up the data. I have 11, I have

04:26 5, I have 6, I have 5, I have 9, I have 7 and I have 5. Now, the first thing is to write them in the order

04:38 of sizes. So, if I am writing this data in the order of sizes, what do I do? I pick from the list,

04:43 from the list here, I have what? I have 5, I have 5, I have another 5. So I have 3, 5. Then I have 6

04:52 followed by next is 7, then the... Now, what if I don't have rearranged it in the order of sizes?

05:02 With this, it is easier to get the mean. So, the mean now would not be the middle value. Now,

05:07 how many values do I have all together? I have 1, 2, 3, 4, 5, 6, 7. So the middle value will just be,

05:13 what would be the middle value? We have 7 values, like I said. So I would say 1, 2, 3, the first 3,

05:19 1, 2, 3, the next 3. So the middle value would give me 6. That's the median. That becomes in an easy pattern.

05:28 Now, let's take in another question. I said find the median in this set of data. That's question

05:37 number 2. Find the median in this set of data. Now, look at the set of data. Like I said, look at it.

05:44 We have 7, 8, 5, 8, 11, 7, 9, 11, 10, and 8. If you look at this data carefully, there are nowhere

05:55 arranged. They are not in the order of sizes. So, step one, like I said, write the values in word

06:02 in an ascending order. So, let's pick it from... Let's pick it from the list. So, picking the data from

06:09 the list. What do we have? We have already we have 7, we have 8, we have 5, I have 8, I have 11, I have 7,

06:21 I have 9, 11, 10, and 8. Now, we are in them in the order of sizes. But when the order of sizes,

06:34 what do we, what are we having? We are having 5, I have 7, the next value follows 7, 7. Well,

06:41 the next value after 7 is 8. 8, and I have the value 8, I have the next one 8, the 3, 8, I have 9,

06:52 and I have 10, followed by 11, I have 11, 2. How? What does that mean? It means that I've been able to

07:01 arrange the values in the order of sizes, starting from the list to the highest value. Now, so, it is

07:09 more easier at this point to get my median. Now, find the middle value, we have 10 values, and this

07:17 is an even number of what values. So, the middle value lies between the 5th and the 6th. The 5th is 8,

07:25 and the 6th is also what? 8. Now, what is that? It simply means, look at this value. First, you count,

07:33 how many values do we have altogether? 1, 2, 3, 4, 5, 6, 7, 8, 9, and I have 10. Now, they say,

07:40 need to be able to break them into 2 equal parts. So, breaking into 2 equal parts, I will simply have

07:46 1, 2, 3, 4. I will have 4. I will simply have 1, 2, 3, 4, and I have another 4. So, I have 2

07:56 middle values. These are the 2 values. Now, these 2 values make them out. So, I will simply say,

08:04 my median is the 2 middle values. 8. Second one plus 8. Then, I divide by 2. So, when I have 8 plus

08:15 8, that would give me divided by 2. 8 plus 8. That would give me 16. So, I will just simply say,

08:21 16 divided by 2, I will still have my word 8, I said. It's asked to be balanced. So, when it is

08:30 balanced, it is more easier in that pattern. Remember, the first one, we have a one which,

08:35 it's an easy goal. But the second one is the one that you have a 2. So, we move to the mode,

08:41 the mode. Now, what's the mode? The mode is the value that occurs most often in a set of values.

08:47 I mean, it is the most common and most popular value. The most common in a set of value

08:54 are the most popular. The most popular is called the mode. Now, in some set of data, all the data

09:02 items are different. In this set, there are no modes. We could have a set of data where no one

09:10 tends to stand out. When no value stands out in you put in itself, then it's possible you could

09:17 have the mode. Or set set of data have more than one mode. It's very much possible. Or some set of

09:24 data have more than one or two modes. Now, look at the value I have on the board. Now, that's question

09:31 number three. I will give me a clear one. Look at the value. Instead, find the mode of the following

09:37 set of data. Find the mode of the following set of data. If you are looking for the mode,

09:44 something interesting about the mode is that the mode is not in order of sizes, not like the median.

09:50 The mode you could just look to and look at the value that is most popular among the set of values.

09:56 So, we have find the mode of the following set of data. Now, we have six. We have nine. We have

10:02 ten, eleven. I have seven. I have five. I have eleven. I have seven. I have nine. And I have eleven.

10:10 I have the last number seven. Take for instance, I said, write the values in an ascending order.

10:17 You could also feel fit in the following process. So, pick in the value. Write them in an ascending

10:23 order. Let's put the values down in the ascending order that they would be. I will have five. I will have

10:29 six. That's question number three. I will have six. I will have seven. I have seven. I have seven.

10:37 Two to seven. I have nine. Nine. I have double nine. I have a single ten. I have double eleven.

10:46 Now, I said, find the value that appears most. If you look at this set of distribution carefully,

10:53 what did you observe? I have seven appears tries. This is double. This is double. So, the mode,

11:02 I will simply say my mode for this distribution is what is seven. Because seven has the highest

11:09 number of frequency or the popular number among the set of distribution. Now, good and fine.

11:16 We move to the next after mode is the mean. Now, the mean gives the average simply average. So,

11:25 when you, wherever your calculation is saying, calculate the mean, the first thing that comes into

11:32 your mind should be average. I'm looking for the average. So, I just say I'm looking for the mean.

11:37 So, the mean gives the average of his data set to work out the mean of a set of values.

11:44 You add up the values and then divided by the own number or how many values you have.

11:50 The total number of values that you have, then divided by the number. That's the mean.

11:55 The mean is the sum of the values divided by the numbers of the values. So, it means that if I

12:01 am to get my mean from any, like I said, if I'm getting, if I'm going to be looking for my mean,

12:07 I would just say the sum of value, that is, no matter the values, I can have sum of x over n. So,

12:15 if I have a lot of x, x could be x1, x2, x3, x4, sum of the values that I have over the numbers of n.

12:23 So, I said divided by the total numbers of the values, when the values are measurable.

12:29 So, make sure that the units are in the same before you can carry out the calculation. Now, we have

12:36 question number four. Sunshine bought 10 different packs of not from the market.

12:42 Sunshine bought 10 different packets of not from the market. Now, she counted the not in each pack

12:53 and found that they had what, 15, 15, 19, 20, 18, 20, 17, 15, 21 and 20 not.

13:06 When she counted the not. Now, it decided to put all the nots together and to then share the total

13:16 number out, equally, between the 10 world packets. Now, how many nots should she put in each packet?

13:26 As a stats, when you see this kind of question, buying a 10 packet. Each packet did not have the same

13:34 distribution. Now, she had to bring out everyone out every of the not out of the packets.

13:41 Now, the question is, how will she rearrange it back into each pack? Now, when you see a question

13:48 like this, that's it's a mean. The question asks you to get what? The mean. And how do I say it?

13:54 Like I said previously, that to get your mean is simply adding the total number of values. So,

14:00 I would just simply say, my mean would give me adding total number of values. That would give me

14:06 15 plus 15 plus addition. I have 19 or the total number of parts. 20, addition, 18 plus I have 20

14:22 addition to I have 20 plus 18 plus 20 plus 17 plus 15 plus 21 plus 20.

14:48 That gives me my sum total to be what? 120, 180, sorry, 180. Now, the question is,

14:57 is 180 my mean? No. 180 is the summation of the total numbers of nots in the 10 packs.

15:06 Now, what would now be my mean? Using the formula for the mean. Like I said, some of the values

15:13 over total number. So, what would now be my, now, this mean that sunshine but should put 18.

15:21 Now, before you can get 18, what you need to do is that my mean would give me

15:26 total number of values. That is 180 over how many packs this sheet of fluid form? 10 packs.

15:39 So, when I divide 0 by 0, I would have 18. So, she should put 18 in each pack, because that should be

15:48 the average for each pack. So, she should put 18 in each of the packs. So, when she packs, she should

15:54 put 18 in each of the 10 packs. So, it could go round. Now, the root on the next stage is finding

16:02 the 3 measure of central tendency. When you are given a particular value, a particular value may

16:07 be required to find the three mean, the three values or the three two in measure of central tendency.

16:14 Now, let's pick the question. That's its example number five. He said, the following set of

16:18 data, 7, 6, 10, 11, 9, 6, 5, find the three measure of central tendency for this set of data, the three.

16:30 Now, what I did in the last few slides, I've been able to separate them, but some questions will

16:36 require you to combine the three together and solve them. So, we are looking for the three,

16:41 calculating for the mean, a calculate for the mean. Remember, the mean is the summation of the

16:47 value divided by the total number of value. That's this now question number five. So, if I'm going

16:54 for the mean, what would I just simply say, I would simply say, the first one, seven plus

17:01 six plus ten plus eleven plus nine plus six plus five over total number. What the total number

17:14 we have? Total number is how many is present? You count. One, two, three, four, five, six, seven,

17:21 divided by seven. So, my mean would give me, total number would give me 54 divided by seven.

17:32 So, I will have it as what? Seven point, seven point, seven one, seven point, seven one.

17:42 That is the first value from the collection. The first two is the mean. Now, if I'm to find the

17:51 next one, which is the mode, that to find the mode, the median, the data needs to be arranged in

17:59 an ascending order. That means we need to arrange them in sizes. So, picking it out. So, how quickly

18:07 we arrange, how have, we are arranging, we are arranging the data. So, when I rearrange,

18:15 I will simply have, we are arranging the set of data, would give me, would give me,

18:24 now let's rearrange it together. We're going to be having five, we're going to be having six,

18:29 nest six, I'm having seven, I'm having nine, ten, and eleven. Now, if I'm to pick with, start with my mode,

18:41 there are which appears most in this set of distribution. The value, the mode, the one that appears most

18:49 in distribution, you will see that six appears twice. So, my mode gives me a six. Now, what would be

18:58 my median? My median, before you get your median, the first thing to do is to, we have, we've

19:04 rearranged it, you count, one, two, three, four, five, six, seven. So, it could easily be divided into three.

19:10 So, I'll have the first three out and the next three out. So, I would simply have my median,

19:16 would give me seven. Just one question, would be able to produce the six of three, that's the name.

19:27 Then the last on the collection is the range, the range. Now, what does the range mean? Or, what

19:34 do we talk about the range? You said the, in measure of central tendency, like the median mode and mean,

19:40 gives you two, three, or sometimes, a few value that summarizes the data. Now, a measure of spread,

19:47 is another way of summarizing what is set of data tells us. A measure of spread tells us how spread,

19:55 spread out the data are. For example, there are the two set of data that we have here. How are these

20:01 data spread out? The data are arranged in and what, in an ascending order. How do they spread out?

20:08 The only way to get out the data spread out is to do for the range. The range is simply the

20:16 highest value minus the lowest value. So, if I'm going to be looking for my range, I would just

20:23 simply say my range is highest, my highest value, my highest value minus my lowest value, the lowest

20:34 of the value, highest minus lowest. So, when I have this behind, so it's a goal. Now, if you look at

20:44 the first set of data, what's the lowest? The lowest my range would give me the lowest here,

20:50 the highest in this set of data is 17. Subtracted for my lowest, which is 13.

20:56 So, my vinyl answer would give me 4. Likewise, I have performed the same operation for the second one,

21:05 my range, my range would give me the highest value. And what is the highest here? The highest

21:15 here is 27. So, minus what is the lowest value, the lowest value is 4. So, my range here is 23.

21:24 Now, looking at it carefully, that gives you an idea of what you are to do when it comes to what

21:32 the range. Now, I've looked at the mean, median mode and the range. It is time to do your

21:40 evolution. Now, the evolution question says, for the set of data given below, 11, 9, 10, 7, 6,

21:49 5, 9, 7, 5, fine, the median, the mode, the range, and the what, the mean. I will be taking for

22:00 the set of data given, we give 11, 9, 10, 7, 6, 5, 9, 7, 5, fine, median, the mode, the range,

22:14 and the mean. The four that we have just treated. Thank you very much. I've come to the end of the class.

22:22 Aluminum Oyase, Sunday.