00:02 Good day, my name is Mr. Afeez.

00:15 I'll be taking you furthermath

00:16 and the topic is the measure of location.

00:19 At the end of this topic,

00:20 you should be able to understand how to find the main,

00:24 the median and the moat,

00:25 and how to find the dencile, percentile and quartile,

00:30 a measure of central tendency.

00:33 So we can also call measure of location

00:36 as measure of centra tendency.

00:38 This is a measure of how the data or information

00:41 are centrally placed.

00:43 Place, the three common names,

00:47 measure of centra tendency,

00:48 depending on the information required,

00:50 had the arithmetic mean, median and the moat.

00:55 Measure of centra tendency

00:58 can also be called measure of location.

01:01 Now, let's define mean median moat.

01:03 Mean, it is the most widely used measure of dispersion

01:09 or measure of location.

01:12 And it's some type,

01:13 we can also call it arithmetic average

01:16 or arithmetic mean.

01:17 The mean of the number,

01:20 that is when you have your X1,

01:23 when you have X2 up to when you have Xn,

01:28 we can find the mean of that by using the formula,

01:34 X bar equals summation X all over n.

01:38 Where your summation X,

01:42 where summation X is the sum of all the items,

01:47 the sum of all this X1 up to Xn.

01:50 And when did that time involve frequency?

01:53 The sum of X1, X2 up to Xn.

01:58 And when did that time involve frequency?

02:01 That is when you have X1, X2 up to Xn,

02:06 and you have a frequency F1,

02:11 F2, F3, up to Fn.

02:14 The formula is going to be different from this

02:16 when you do not have a frequency.

02:18 And the formula is X bar all over summation F,

02:23 X all over summation F.

02:26 So this is when you have a discrete,

02:31 I mean when you have continuous,

02:32 and this is when you have a discrete.

02:35 So the formula is different.

02:39 How, what is medium?

02:43 This is the medium value of a set of data.

02:48 For example, if you have,

02:50 you have your X1, your X2 up to Xn.

02:55 When this number is arranged in ascending order,

02:58 and that is when we have,

03:00 the medium number when it is arranged in ascending order

03:03 is what we call a medium.

03:05 Mood, Mood is when you have a set of data,

03:15 and the one that's occured most in this.

03:19 If for example you have two, three, three,

03:22 one, five, three,

03:25 you can see that in this number,

03:29 the set of data that we have,

03:31 three occured three times more than others.

03:35 So this is the mode.

03:36 So mode EA is what equals three,

03:40 because it's occured three times more than other numbers.

03:44 And you can also have more than two Mood.

03:47 If for example you have two,

03:50 two, three, three, five, one,

03:56 you can see that two occured two times,

04:01 three occured two times.

04:02 So we can have, our Mood can be,

04:04 can be words two and three.

04:06 So we can have more than two Mood in a set of data.

04:14 [BLANK_AUDIO]

04:18 Now let's look at example number one.

04:20 [BLANK_AUDIO]

04:23 Calculate the main medium and mode of the numbers.

04:26 You have 18, 20, 25, 30, 32,

04:36 [BLANK_AUDIO]

04:39 25, 28, and 15.

04:42 And we want to calculate the main.

04:46 We first of all, and you know the formula for that.

04:53 That is summation x all over n.

04:57 So we had all this, and that is 18 plus 20 plus 25 plus 30 plus 22 plus 25 plus 28 plus 15.

05:12 We all over the number of data, that is the number of these 1, 2, 3, 4, 5, 6, 7, 8, all over 8.

05:23 And that's give us 22, that is 1, that is 1, that is 1, 8, 3, all over 8.

05:35 And that will give us 22.9 approximated to the nearest old number we have 23.

05:40 So our main equals 23.

05:44 [BLANK_AUDIO]

05:48 Now a median, don't forget we say that when you want to find the median,

05:53 is that you arrange it in ascending or descending order?

05:56 That is from the smallest to the I.

05:59 That is ascending and from the I is to the smallest, that is descending.

06:04 So let's arrange this number, let's arrange the number in ascending order.

06:10 So we have 15, 18, 20, 22, 25, 25, 28, and 20, and 30.

06:25 And this is arranging in ascending order from the smallest to the I.

06:32 And the median, after arranging, the median after arranging in ascending order will be,

06:43 you can see, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8.

06:50 You can see that these are the two numbers that's in the middle.

06:55 After we arrange it in the words, in ascending order.

06:59 So it means, and whenever you have two numbers at the middle,

07:04 it's possible for us to have a number.

07:06 So when you have a number, the number is going to be a median.

07:10 But in the case whereby you have two numbers, is as your middle number,

07:15 when arranging it in ascending order.

07:18 You are going to have the two number and divide it by two.

07:20 That is, 22, all of us 25, I mean 22 plus 25, all of us two.

07:28 And that would give us 47, all of us two.

07:32 And that is 23.5.

07:35 Approximately, we have 24 as our median.

07:40 Then, merge.

07:42 Don't forget that we said more these words.

07:45 The one that occur most in the set of values.

07:49 That occur most in the set of values.

07:51 And that is, you can see that five only occur ones,

07:56 continue occur ones, 20 occur ones, 22 occur ones, 25 year, 25 year.

08:00 So 20, 25 occurs two times, what's 28 occur one time, 30 occur one time.

08:05 So it is only 25 that occurs two times more than the order number.

08:10 So therefore, merge equals 25.

08:15 Now, let's look at this example.

08:23 Number two, that has a frequency table.

08:26 And we can use this also to find mean median and merge.

08:35 We have the number of suitcases, which is 0, 1, 2, 3, 4, 5.

08:40 And we have the travellers.

08:42 And this is, we have to calculate our mean.

08:47 We are going to have what we call a frequency table.

08:53 That is our x, we have our f.

08:57 Our x is the number of suitcases, which is 0, 1, 2, 3, 4, 5.

09:05 And frequency is the travellers, which is 2, 7, 7, 2, 3, 9.

09:16 And don't forget, we said, when we want to find the mean,

09:20 when we have a frequency table, the formula is

09:23 going to be quite different from when you have just ordinary numbers.

09:28 And that is the reason why we have this true table.

09:31 So we have-- and don't forget that the mean is of a frequency

09:36 table is summation f x, all over f.

09:41 So we have our f x.

09:44 So that is f times x.

09:47 So 0 times 2, we have 0, 1 times 7, we have 7, 2 times 7,

09:52 we have 14, 3 times 2, we have 6, 4 times 3, we have 12.

09:57 And 5 times 9, we have 45.

10:00 The addition of all these, when you had all these, 7 plus 14,

10:05 21 plus 6, 27, 27 plus 12, 27 plus 12, we have 39.

10:14 And the summation of that gives us 84.

10:19 Why this summation of f give us 30?

10:24 So therefore, summation f x equals 84, y summation f equals 30.

10:42 So we have mean x bar to be 84, all over 30.

10:51 And that will give us 2.8.

10:56 When we are going to the nearest one number, we have 3.

10:58 So therefore, what mean x bar is 3?

11:03 Now, let's calculate the medium.

11:05 I mean, the medium, the medium.

11:11 And how do we calculate the medium?

11:13 Medium will be calculated when the number is arranged

11:17 in ascending order.

11:18 And this is already arranged.

11:20 It's already arranged in ascending order.

11:22 You can see.

11:24 And that is, we have 0, 1, 2, 3, 4, 5.

11:28 If you look at this, you see that there's only 2 and 3

11:34 that occur in the middle.

11:36 And that is the medium.

11:38 And these two numbers occur in the middle.

11:39 And therefore, medium will be 2 plus 3, all over 2.

11:48 And that will give us 5, all over 2.

11:51 And that is 2.5.

11:55 Approximately, we have 3.

12:01 That is the medium.

12:02 And then, to calculate mode, to calculate mode,

12:08 mode is the number that occurs most,

12:13 that occurs often in the set of data.

12:16 And if you look at this data that we have,

12:20 if you look at this data that we have,

12:22 what we see is that 0 occurs 2 times, 1 occurs 7 times,

12:29 2 occurs 7 times, 3 occurs 2 times, and 4 occurs 3 times,

12:35 and Y5 occurs 9 times.

12:37 You can see that 5 occurs 9 times more than other numbers.

12:45 So it means mode is going to be, therefore, mode equals 5.

12:55 So that is how to calculate.

12:57 Me, median, and mode, when you have a frequency table.

13:03 So let's look at how to calculate the side, percentile,

13:08 and cotile.

13:10 And these also are the measure of the center,

13:19 measure of location, the measure of location.

13:24 And the first one is cotile.

13:27 How do we calculate cotile?

13:31 How do we calculate cotile?

13:33 The formula for calculating cotile is qi class equals n

13:42 high all over 4, the value of observation,

13:53 and the, if for example, you have your ns to be 2,

13:59 it means we have 2, and your qi is going to be L

14:11 plus n high all over 4 minus SCF, everything all over F times

14:23 C. What is your L?

14:25 What is your I?

14:26 What is your CF?

14:28 What is your F?

14:29 And what is your C?

14:30 Where your I can only be 1, 2, 3.

14:36 It means that, what does that mean?

14:38 It means you can only find q1, q2, and q3 when you're

14:44 talking about cotile.

14:45 You cannot find 4th cotile.

14:47 There's nothing like 4th cotile.

14:48 There's nothing like 5th cotile.

14:49 You can only find your 4th cotile, 2nd cotile,

14:53 and the 4th cotile.

14:53 Let's, the decimal, the decimal.

15:01 The formula is d i class equals the i n all over 10,

15:07 value of the observation.

15:09 And the formula is d i equals your L plus i n all over 10

15:15 minus CF, all over F times C.

15:19 Where your I can only be 1, 2, 3, up to 9.

15:23 Meaning that, you can only find the 4th decide, 2nd decide,

15:28 4th, up to 9, that's the side.

15:31 You cannot find 10's decide.

15:33 Then percentile, percentile.

15:41 The formula for that is P i class equals i n all over 100.

15:46 And the value of, the value of observation

15:50 and the P i equals L plus i n all over 100 minus CF,

15:59 all over F times C.

16:02 And your high can only stick value from 1 to 99.

16:05 Meaning that, you can only find the 4th percentile,

16:09 the 2nd percentile, the 50 percentile.

16:12 You can only, and also, you can find 99.

16:14 You cannot, you cannot find 100 percentile.

16:17 You know, from the word percentage.

16:18 That is where the percentile comes from.

16:23 So now let's look at this example to find our design,

16:27 called size, and percentile.

16:32 Now, we are given this, the class of the class

16:38 and the frequency.

16:39 And we are asked to find the total code type, the 7th decide,

16:43 and this 20, 28 percentile of the following group of data.

16:48 And we have the class, which is 2 to 4.

16:52 We have 4 to 6, and we have 6 to 8, and we have 8 to 10.

16:57 2 to 4 occurs 3 times, and 4 to 6 occurs 4 times,

17:02 and 6 to 8 occurs 2 times.

17:04 Why 8 to 10 occurs 1 times?

17:06 And then we find the total code type and the second,

17:09 I mean, the 7th decide and the 20th percentile of this set of data.

17:19 Now, we are going to have a table called a cumulative frequency table,

17:28 a cumulative frequency table.

17:29 Whenever you have your CF, your CF mean cumulative frequency,

17:36 cumulative frequency.

17:40 So whenever we have a cumulative frequency in the table,

17:44 such table is called cumulative frequency table.

17:48 When we don't have a cumulative frequency table,

17:50 it is only just a class and a frequency.

17:53 We call that table a frequency table.

17:55 So now, we are to find the first one is to find the total code type.

18:05 And that is Q3.

18:07 It means our i equals 3.

18:12 From the formula, Q i equals n i all over 4 value of observation.

18:25 And the formula also get i is Q i equals l plus n i all over 4 minus CF all over F times C.

18:43 And the total code type we have to find is 3.

18:47 Our high is 3.

18:47 So it means wherever you see i, we are putting 3.

18:51 So we have it means we have Q3 equals 3 n all over 4.

19:02 And our hand from this is what is 10.

19:05 From the table addition of all these of frequency table we give us n.

19:12 So it means we have 3 times 10 all over 4.

19:18 And that will give us 30 all over 4.

19:23 And 30 all over 4 will give us 7.5, 7.5 value of observation.

19:34 So it means what does that mean?

19:37 What does that mean?

19:38 It means our Q3, our Q3 equals 7.5 value of observation.

19:46 So our Q3 is from this cumulative frequency table.

19:53 So it's from this very one.

19:55 That is our Q3.

19:56 So now therefore Q3 will now be l from the formula, l plus.

20:04 So we have the all over this one is going to be 7.5 now.

20:09 So we have 7.5, we have l plus 7.5 minus CF all over f times c.

20:27 What's our health?

20:29 What's our health?

20:31 Our health is lower class, lower boundary points of the Q3 class.

20:41 What is lower class boundary of the Q3 class?

20:47 Don't forget what we said 7.5 value of observation is at V8, is at V8.

20:57 This is V8 is 7.5 lies.

21:00 You know we have 6 to 7, I mean 6 to 8 rather, and 7.5 lies within 6 to 8.

21:06 So this is where the Q3 falls, this is where the Q3 falls.

21:11 So our L is called the lower, we call, when you have a number in form of this, we call

21:18 this a lower value, why this is upper value?

21:22 We call this a lower value, we call this upper value.

21:26 So the lower boundary points of the Q3 is 6, so we have 6 here, you want to understand

21:35 that though.

21:36 So this is our C, I mean we have L to be 6, Y CF, which is our cumulative frequency.

21:43 How do we find cumulative frequency?

21:46 Your cumulative frequency can be found from a frequency table, from this frequency, and

21:54 that is you write the first 3 of your frequency, you write it down, and you have 4 to 8, we give

22:02 you the second one, when you have 2 to 8, 3 plus 4 we give us 7, and 4, 7 plus 2 we give

22:10 us 9, and 9 plus 1 we give us 10.

22:14 If the last number of your frequency of your cumulative frequency is not the same thing

22:17 as the total number of frequency, then you are not getting this.

22:21 Note that the last number of your cumulative frequency must be equal to the summation

22:26 of the frequency.

22:28 So it means our cumulative frequency and our SAV is what?

22:35 Our CF is going to be cumulative frequency before the 7, before the 7.5 value of the

22:43 observation.

22:44 And what is that?

22:45 The cumulative frequency before the 7.5 value of the observation, this is.

22:51 Before that, before this is the 7.5 value of observation, this is the Q3, but before that

23:01 is going to give us our cumulative frequency.

23:03 So we have cumulative frequency to the world to be 7, and our C, we have the frequency,

23:11 that is the frequency of the, that is the frequency, that is the frequency of the 7.5

23:20 value.

23:21 And that is give us 2, and that is give us 2, that is give us 2.

23:30 So frequency is 2, so therefore our Q3 and our C is the class, is the class width, which

23:38 is also 2.

23:39 How do we find the class width?

23:41 That the difference between these 2 and 4, the difference between these 2 and 4 is 2.

23:47 The difference between these 1 is also 2, the difference between these 2 is also 2.

23:50 So that is our class, the same as the same thing all true from our class.

23:54 So that is what we call the class, that is the, the, the width of the, of the class.

23:59 So we have, that's, so therefore our Q3 now can be 6 plus 7.5 minus 7, cumulative frequency

24:14 all over 2 times 2, and that will give us 6 plus 7.5 minus 7 will give us 0.5.

24:33 So 0.5 all over 2 times 2, this we can't do this, so we have 6 plus 0.5 and that is 6.5.

24:44 So therefore our Q3 is 6.5.

24:50 Now, how to find the 7's, the 7's, the 7's, and the formula, you know, that's, the formula

25:00 is Q, I mean, it's going to be d, high equals, n high all over 10, value of observation,

25:14 and therefore we can have our d high, can have our d high to be L plus n high all over 10

25:30 minus cumulative frequency, all over frequency, everything times C. And it means our high A is

25:40 7.

25:41 Now, this 7 equals, that is 7, n all over 10, and our n is 10, don't forget, so we have 7 times

25:58 10, all over 10, and that is 10, we have 7's, 7's, or value of observation, so that is,

26:13 so it means, therefore this 7 is going to be L plus 7 minus cumulative frequency, all

26:22 over F, everything times C. And we have our L, it is the lower boundary points before the

26:39 d 7 class, and what is that?

26:42 And it means, 7's value of observation of cumulative frequency of cumulative column,

26:47 and that lies between 4 and 6, if you look at it, you will see that the 7's value of observation

26:56 line between 4 and 6, so that is, so this is going to be one of, so and our L which is

27:03 the lower boundary points, and 4 is the lower boundary points, so we have L to be 4, we have

27:10 a cumulative frequency of that, before this 7 class, that is 3, and we have our F, that

27:20 is the frequency of that class of the d 7 class, and that is 4, and we have our C to be 2,

27:28 so therefore, therefore, this 7 is going to be 4 plus 7 minus cumulative frequency 3,

27:41 all over F, 4, everything times 2, we have 4 plus 4 all over 4 times 2, so this would be,

27:57 if you consider this we have 1, so 1 times 2, that would be 4 plus 2, and that is 6, so therefore,

28:05 our d 7, the 7's total, d 7, which is the 7's, the 7's size equals 6, and the last one,

28:20 which is the 20th percent time, and from the formula, which is a p high equals n high

28:34 all over 100, value of observation, and our p 20 now is going to be 20 n all over 100,

28:50 and our n is 10, so we have 20 times 10 all over 100, so this is going to be the second

29:10 value of observation, so p 20 is going to be second value of observation, that is the second

29:17 value of observation, and that is 2 to 4, that is 2 to 4, so in that case, we have our,

29:32 we have p 20 to the l plus 2 minus cumulative frequency all over F all times, that is 2 minus

29:55 cumulative frequency all over F all times C, so our l, which is the lower boundary of

30:05 data, and that is 2, and our CF, the cumulative frequency of that class, and that is before

30:15 that class is 0, and the frequency of that class is 3, and that C is 2, so therefore, we have

30:28 our p 20 to be 2, which is our l, 2 minus cumulative frequency which is 0 all over F, and

30:41 that is our F is 3 times 2, so this is 2 plus 2 all over 3 times 2, and we have 2 plus 0.33,

30:56 that is 2 divided by 3, we give us 0.333, then multiply by 2, so we have 2 plus, multiply

31:04 this 0.33 by 2, we give us 1.33, and that will give us 2 plus 1.33, we give us 3.33, and

31:14 that is our p 20, that is our 28 percentile, now having understood how to calculate the main

31:24 medium mode, and how to calculate the decil, the percentile, and the quartile, we have this

31:29 solution, the first one is, we have to calculate the main medium mode of the numbers, and that

31:34 is 35, 28, for the 228, 56, 70, 35, and that is for a continuous values, then when you have

31:45 our second one, calculate the main medium and mode scores, represented in the table below,

31:52 this is the frequency table, so the main of that will be quite different from that

31:56 the first one, and the last one, we have took up, we, the numbers of matches in 100 busses

32:04 are contained, and the result are shown in the table below, and that is, this is what

32:10 we call the group, frequency, group data, so 25, the number of matches is 25 to 28, 29

32:17 to 35, 32 to 36, 37 to 40, and we have the number of busses, and which is the frequency,

32:23 18, 34, 37 and 11, so we have to calculate the first quartile, the 7 decil, and the 58 percentile.

32:32 Thank you for watching, my name is Afeez, till next time.