Measures of Center - By Anywhere Math
Transcript
00:0-1 | Uh huh . Welcome to anywhere , Math . I'm | |
00:01 | Jeff Jacobson . And today we're gonna talk about the | |
00:03 | measures of center more specifically the mean , median and | |
00:08 | mode . Let's get started . Before we get to | |
00:28 | the first example , let's talk about what exactly a | |
00:30 | measure of center is a measure . Center is just | |
00:33 | a measure that describes a typical value for the data | |
00:38 | set . In other words , if I gave a | |
00:40 | test and I've got 100 students and I have all | |
00:45 | the scores for all of the students on the test | |
00:47 | and I'm wondering , well , how did they do | |
00:50 | ? How did my students do on that last test | |
00:53 | ? It's going to be really tough to tell when | |
00:55 | I have 100 numbers , 100 grades . Uh , | |
00:58 | just looking at them all together . So instead we | |
01:01 | use things like median mean and mode to get a | |
01:05 | better idea of a typical value . So instead of | |
01:10 | 100 numbers , I might have The mean was an | |
01:14 | 85 , right ? That's the average . Okay , | |
01:19 | that gives me a better idea of how the students | |
01:21 | did . So that's what measures of centers are . | |
01:24 | They're just taking the data set and finding a typical | |
01:26 | values kind of somewhere in the middle uh to give | |
01:30 | you a better understanding of the data . So let's | |
01:32 | get to example one . All right , here's example | |
01:35 | one . What is the mean number of messages sent | |
01:38 | ? So here's our data . Uh So we're finding | |
01:41 | the mean . That's gonna be the first measure of | |
01:46 | center that we're going to talk about . So first | |
01:48 | what is mean ? Another word for that is the | |
01:51 | average . Okay . Finding the mean of a set | |
01:58 | of data is the same thing as finding the average | |
02:00 | of that data . And to do that , all | |
02:03 | you do is you take the some of the data | |
02:08 | divided by the number of values . Yeah . Okay | |
02:15 | . So you add them all up , that's the | |
02:17 | sum then . You divided by how many pieces of | |
02:20 | data there are . So let's do that . Um | |
02:23 | First thing what I like to do it's a good | |
02:27 | thing when you're doing things like mean median mode . | |
02:29 | The very first step is to put all the data | |
02:32 | in order . So if I'm looking from least to | |
02:35 | greatest well 82 is my least . Um Then let's | |
02:39 | see Mm We've got 90 and the good point . | |
02:48 | And finally on 25 just double check I checked them | |
02:53 | all so I'm just gonna double check by counting them | |
02:56 | . So I got 12345671234567 Perfect . Okay so I | |
03:03 | got him off there in order . That's the first | |
03:05 | step . Now I'm gonna add them , I'm gonna | |
03:07 | find the song . I've got 721 as my son | |
03:14 | . Now I just divided by the number of values | |
03:17 | . Again there were 123-4567 . So 721 divided by | |
03:23 | seven . When I divide , that's gonna give me | |
03:27 | 103 . So my mean is 103 text messages again | |
03:39 | , that's like the average 103 Text messages . Here's | |
03:45 | some to try on your own . Alright , example | |
03:54 | to we're gonna have three parts of this example at | |
03:57 | A B and C . So first a identify the | |
04:00 | outlier . Well here's our data , the height of | |
04:03 | ponies and inches . First what is an outlier ? | |
04:08 | So an outlier ? Let's write this down . Boom | |
04:15 | is a data value that lies kind of outside all | |
04:19 | the other values . So what that means is an | |
04:21 | outline is a data value that is either a lot | |
04:28 | greater than all the other values or a lot less | |
04:31 | . It's kind of outside the other ones that is | |
04:34 | either a lot greater . Four left dandy the other | |
04:40 | night . That's an outlier . Okay , so first | |
04:46 | like always I'm gonna put my data in order and | |
04:48 | that's going to help me see if there's any outliers | |
04:51 | . Just to double check let's count . 123456789 10 | |
04:57 | 12345 times two is 10 . Okay so I got | |
05:01 | all my data in order . Now let's take a | |
05:02 | look if I wanted to , I could make a | |
05:05 | dot plot and that could help me see if there's | |
05:07 | any outliers but hopefully looking here it should be obvious | |
05:12 | . Can you see what the outlier is ? Well | |
05:15 | if you notice we go from 28 all the way | |
05:17 | up to 37 , 37 , 39 , 42 . | |
05:23 | Here the data is all clustered pretty close together Except | |
05:28 | the 28 , is quite a bit less than all | |
05:31 | the other values , which means my outlier is 28 | |
05:38 | . Okay , let's try part B . Okay , | |
05:41 | Part B is just find the mean . So again | |
05:44 | the mean is the sum of all your data values | |
05:46 | divided by how many values there are . So if | |
05:49 | we add all of this up and hopefully you get | |
05:52 | 379 , that's what I got . Uh So that's | |
05:57 | the some I'm going to divide that by how many | |
05:59 | there are . So 123456789 10 . There's 10 values | |
06:05 | which is really nice because divided by 10 I can | |
06:08 | just move the decimal place once to the left . | |
06:10 | So my mean then is 37.9 . Remember my units | |
06:16 | ? All these values were inches , so 37.9 inches | |
06:22 | . Okay , So the mean of the heights of | |
06:24 | the ponies is 37.9 in . Let's try the last | |
06:28 | part . Part C . All right , here's part | |
06:30 | C . Of example to find the mean again . | |
06:32 | But this time without the out letter . So if | |
06:35 | we remember our outlier was 28 , so I'm gonna | |
06:39 | find it without that that we're not going to include | |
06:42 | that . Okay ? Um so now if again fined | |
06:46 | the sum of all the data right ? 379 -28 | |
06:51 | because we took it away , I'm going to get | |
06:53 | 351 ah divided by . Now notice there's still aren't | |
07:01 | 10 values , we got rid of the outliers . | |
07:03 | So now there's only nine values , so I'm dividing | |
07:05 | by nine And let's see nine into 35 Goes three | |
07:11 | times . Then there's 8 81 39 . Uh and | |
07:16 | that's again 39" . So that is my uh , | |
07:22 | I mean without the outlier and notice they're different . | |
07:26 | And the reason if you think about the outlier was | |
07:29 | a lot less than the rest of my values . | |
07:33 | So when I included the outlier in , when I | |
07:36 | was calculating the mean , you can think of it | |
07:38 | as it's bringing down that mean it's bringing down the | |
07:41 | average if we don't include the outlier notice are mean | |
07:47 | was was greater , it was hired . So keep | |
07:51 | that in mind . When you're calculating mean , the | |
07:54 | outlier , if there are some can really affect your | |
07:58 | mean , they can either make it a lot greater | |
08:01 | than it probably should be or a lot less than | |
08:04 | it probably should be depending on where that outlier is | |
08:07 | . Okay , here's some more to try on your | |
08:09 | own . Okay , Example , three find the median | |
08:19 | and mode of the bowling scores . So we've already | |
08:21 | talked about one measure center , which was the mean | |
08:25 | the other two we're going to talk about today are | |
08:27 | the median and the mode . So first let's discuss | |
08:31 | what exactly is the median ? And the median is | |
08:35 | just the value in the middle . When you have | |
08:38 | all the data in order from left from least to | |
08:41 | greatest . The value that's exactly in the middle is | |
08:44 | called the median . Okay . So yeah , so | |
08:46 | let's write down the value in the middle when the | |
08:51 | data is in order from least grades . Okay . | |
09:00 | So let's write that down . And and I always | |
09:02 | remember it median is the only one out of mean | |
09:04 | median . And mode that has an eye . And | |
09:07 | I think I for middle also has a nice . | |
09:09 | So that can maybe help you remember ? Um Good | |
09:12 | . So that's the median . Well , how about | |
09:15 | the mode ? Mode is pretty simple . The mode | |
09:20 | is just the most common value . Right ? Most | |
09:24 | common value . And again mode has an O . | |
09:27 | I think . Oh for most most and mode . | |
09:31 | Uh So most common value . You can have one | |
09:34 | mode right ? You can have more than one mode | |
09:37 | . If there's a couple that are both occur the | |
09:41 | same amount of times that are much more than the | |
09:43 | others . You can also have no mode . And | |
09:45 | no mode would be where there is exactly one of | |
09:49 | each value . Right ? Not nothing is more than | |
09:52 | the others . Then you would have no mode . | |
09:54 | Um So that's what we're finding first . The very | |
09:59 | first step . Remember put the data in order . | |
10:02 | That's always our first step . So let's double check | |
10:04 | . 123456789 10 12345 times two is 10 . Yes | |
10:11 | . Okay . Now all I need to do for | |
10:15 | the median is find the number that's exactly in the | |
10:17 | middle . If you have an odd number of data | |
10:21 | values right ? It's very easy because there's going to | |
10:25 | be one of those values that are exactly in the | |
10:27 | middle . Think about your hand , right ? Your | |
10:29 | fingers , you have five fingers , which is why | |
10:32 | you have a middle finger , right , odd number | |
10:36 | . This one is right in the middle , you | |
10:38 | got to to the left and you got to to | |
10:40 | the right . Uh So if you have an odd | |
10:43 | number is very easy . You can find the one | |
10:45 | that's right in the middle . Some people like to | |
10:47 | kind of cover up as they go from outside to | |
10:49 | inside or cross off work their way in the middle | |
10:53 | . Um But if you have an even number , | |
10:57 | we won't have a data value that's exactly in the | |
10:59 | middle . So this is what we're gonna do Right | |
11:03 | ? We've got 10 here . So if I'm crossing | |
11:05 | them off work my way to the middle notice now | |
11:13 | I've got two values left . So in this case | |
11:17 | what I'm gonna do is I'm going to find the | |
11:19 | value that's exactly in the middle of those two . | |
11:22 | And to do that sometimes you can do some mental | |
11:25 | math and just know another way is just to adam | |
11:28 | and then D . Vitamin too . So 100 and | |
11:31 | 35 plus 1 45 Uh is to 80 , Divide | |
11:40 | that by two . And I get 1 40 right | |
11:44 | ? And if you look 135 and 1 45 . | |
11:47 | Yeah 1 40 is exactly in the middle of those | |
11:50 | two . Uh So 140 is my median exactly in | |
11:56 | the middle . Okay let's check out the mode . | |
12:00 | Now again the mode is the number that occurs the | |
12:03 | most often the most common number . So notice all | |
12:07 | of these ones only happened once , but then we | |
12:09 | get to 160 and there's 2 160s . So that | |
12:14 | is my mode . Mode is going to be pretty | |
12:16 | quick . So the mode is 160 . Also with | |
12:22 | motives kind of nice because that's the only measure of | |
12:25 | center that you can use when you have data . | |
12:28 | That's not numbers . So if you have , if | |
12:31 | you're doing a survey and you're thinking , okay , | |
12:32 | what are students favorite colors ? Uh , and they | |
12:36 | give you all their favorite color is blue and green | |
12:38 | and purple and things you can't find the mean of | |
12:41 | all the colours . You can't find the median of | |
12:43 | all the colors , but you can find the mode | |
12:46 | which one occurs the most often . So keep that | |
12:49 | in mind when you're thinking of kind of what measure | |
12:52 | of center to use when , Okay , uh , | |
12:55 | here's some to try on your own . Thank you | |
13:04 | so much for watching . And if you like this | |
13:05 | video , please subscribe . Mhm . |
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