WEBVTT mathematics/basic-math/pyo
00:00:00.600 --> 00:00:02.100
Welcome back to Educator.com.
00:00:02.100 --> 00:00:07.900
For the next lesson, we are going to go over measures of central tendency.
00:00:07.900 --> 00:00:18.300
The measures of central tendency are just three different types of ways you can describe data.
00:00:18.300 --> 00:00:22.300
If you have a set of numbers, if you have some numbers,
00:00:22.300 --> 00:00:30.700
then there are three ways you can represent the measures of those numbers.
00:00:30.700 --> 00:00:35.100
The first one, the first measure of central tendency is the mean.
00:00:35.100 --> 00:00:42.800
The mean is the sum of all the numbers divided by however many numbers you have.
00:00:42.800 --> 00:00:44.100
Another word for it is average.
00:00:44.100 --> 00:00:48.900
You are looking for the average of all the numbers in your data.
00:00:48.900 --> 00:00:51.500
The next one is median.
00:00:51.500 --> 00:00:58.600
Median is when you list out all the numbers in order from least to greatest,
00:00:58.600 --> 00:01:01.700
you are going to find the middle number, the one that is right in the middle.
00:01:01.700 --> 00:01:06.700
That is called the median; the key word here is middle.
00:01:06.700 --> 00:01:11.700
The third one is the mode; the mode is the number that occurs the most.
00:01:11.700 --> 00:01:15.200
It is the number that you see the most in your set of data.
00:01:15.200 --> 00:01:19.700
The keyword here is going to be most.
00:01:19.700 --> 00:01:27.200
Let's say if I have a set of numbers, let's say 1, 2, 3, 4, and 5.
00:01:27.200 --> 00:01:34.700
The mean, keyword average, we are going to find the average of all those numbers.
00:01:34.700 --> 00:01:42.100
We are going to add them all up; 1 plus 2 plus 3 plus 4 plus 5.
00:01:42.100 --> 00:01:47.000
You are going to divide by however many numbers you have.
00:01:47.000 --> 00:01:55.000
Here we have five different numbers; you are going to divide that sum by 5.
00:01:55.000 --> 00:01:58.200
1 plus 2 is 3.
00:01:58.200 --> 00:02:02.400
I am just going to write that number on top like that.
00:02:02.400 --> 00:02:10.600
That is 3 plus 3 is 6; 6 plus 4 is 10; 10 plus 5 is 15.
00:02:10.600 --> 00:02:18.400
This looks like a fraction... if I write it like... I am sorry; wrote the wrong number.
00:02:18.400 --> 00:02:21.300
5... if write it like that, it looks like a fraction.
00:02:21.300 --> 00:02:27.700
But fractions are division; you can just think of that as 15 divided by 5.
00:02:27.700 --> 00:02:33.800
15 divided by 5; we know that 5 goes into 15 three times.
00:02:33.800 --> 00:02:39.700
15 divided by 5 is 3; the mean is 3.
00:02:39.700 --> 00:02:44.200
That is the average of those five numbers.
00:02:44.200 --> 00:02:50.300
The median of that set of data is going to the middle number
00:02:50.300 --> 00:02:54.200
but only when you list it out in order from least to greatest.
00:02:54.200 --> 00:02:57.100
You must list it out.
00:02:57.100 --> 00:03:04.400
Here it is already listed from least to greatest; 1, 2, 3, 4, 5.
00:03:04.400 --> 00:03:16.000
The number in the middle will be this number right there; the median is 3.
00:03:16.000 --> 00:03:21.900
When you have two numbers in the middle, let's say you have an even number of numbers.
00:03:21.900 --> 00:03:27.200
Say it is just 1, 2, 3, and 4.
00:03:27.200 --> 00:03:31.900
If that is your data, you have two numbers in the middle.
00:03:31.900 --> 00:03:36.500
Then you are going to find the average between those two numbers.
00:03:36.500 --> 00:03:39.800
We are going to add those two numbers and divide it by 2.
00:03:39.800 --> 00:03:47.000
That will be 2 plus 3 divided by... there is only two numbers there so it is 2.
00:03:47.000 --> 00:03:51.100
That is going to be 5/2.
00:03:51.100 --> 00:03:53.900
You can usually leave it as a fraction.
00:03:53.900 --> 00:03:56.100
If you want, you can change it to a mixed number.
00:03:56.100 --> 00:04:02.800
How many times does 2 fit into 5?--2 fits into 5 two times.
00:04:02.800 --> 00:04:07.800
You have 1 left over; keep your same denominator.
00:04:07.800 --> 00:04:11.100
That is how you change... this is called an improper fraction
00:04:11.100 --> 00:04:15.100
when the number on the top is bigger than the number on the bottom.
00:04:15.100 --> 00:04:23.000
You can change it to a mixed number where you are going to have a whole number and then a proper fraction.
00:04:23.000 --> 00:04:27.600
Again 2 fits into 5 two times; that becomes your whole number, 2.
00:04:27.600 --> 00:04:31.400
Your leftovers is 1 over... your denominator is 2.
00:04:31.400 --> 00:04:32.900
You can leave it like that.
00:04:32.900 --> 00:04:43.200
Or if you want, you can just do 5 divided by 2, and change it to a decimal.
00:04:43.200 --> 00:04:49.900
Remember 5, this top number, goes inside; that is on the outside.
00:04:49.900 --> 00:04:53.100
Put a decimal point at the end of that number; bring it up.
00:04:53.100 --> 00:05:01.500
2 fits into 5 twice; that is a 4; we subtract; get 1.
00:05:01.500 --> 00:05:07.300
I can add 0s there at the end of that number behind the decimal point.
00:05:07.300 --> 00:05:14.100
Bring that 0 down; 2 goes into 10 five times.
00:05:14.100 --> 00:05:17.900
That is 10; my remainder is 0.
00:05:17.900 --> 00:05:30.600
Your median here, when we find the average of that, will either be 2 and 1/2 or 2.5.
00:05:30.600 --> 00:05:33.800
You could just think of it as halfway between 2 and 3.
00:05:33.800 --> 00:05:42.300
That is the average; between 2 and 3 is going to be 2 and 1/2; 2.5.
00:05:42.300 --> 00:05:46.400
The third one, the mode, remember the keyword here is most.
00:05:46.400 --> 00:05:50.300
It is the one that you see the most.
00:05:50.300 --> 00:05:58.700
Here with our set of data, 1, 2, 3, 4, 5, you only see each of the numbers one time.
00:05:58.700 --> 00:06:03.500
In this case, we have no mode.
00:06:03.500 --> 00:06:13.300
If you had 1, 2, 2, and 3, then you know the mode would be 2 because you see that number the most.
00:06:13.300 --> 00:06:16.900
It occurs the most; that is the mode.
00:06:16.900 --> 00:06:26.600
Again mean is average; median is middle; mode is most.
00:06:26.600 --> 00:06:33.600
First example, using this set of data, we are going to find the mean, median, and mode.
00:06:33.600 --> 00:06:37.300
Mean, we are just going to add up all the numbers.
00:06:37.300 --> 00:06:42.900
For mean, it doesn't if the numbers are in order because when you add, the order doesn't matter.
00:06:42.900 --> 00:06:47.500
If I add 1 plus 2, it is going to be the same thing as 2 plus 1.
00:06:47.500 --> 00:07:00.500
Here just add up all the numbers; 3 plus 5 plus 3 plus 8 plus 6 plus 10 plus 4.
00:07:00.500 --> 00:07:10.900
Then we are going to divide that number by 1, 2, 3, 4, 5, 6, 7, seven numbers.
00:07:10.900 --> 00:07:15.900
3 plus 5 is 8; plus 3 is 11.
00:07:15.900 --> 00:07:24.200
That is 19; that is 25; that is 35; that is 39.
00:07:24.200 --> 00:07:33.400
It is going to be 39; that is the sum; divided by 7.
00:07:33.400 --> 00:07:36.000
You can either leave it like this as long as it doesn't simplify.
00:07:36.000 --> 00:07:47.100
As long as there is no factors that goes into 39 and 7, you can just leave it as an improper fraction.
00:07:47.100 --> 00:07:54.100
To change it to a mixed number, we ask ourselves how many times does 7 fit into 39?
00:07:54.100 --> 00:08:01.200
I know 7 times 5 is 35; 7 times 6 is 42; that is too big.
00:08:01.200 --> 00:08:07.400
My whole number is going to be 5 because 7 fits into 39 five times.
00:08:07.400 --> 00:08:14.800
I have 4 leftovers; 4 over... keep the same denominator.
00:08:14.800 --> 00:08:19.400
That will be our mean.
00:08:19.400 --> 00:08:26.200
Again if you want to change this to a decimal instead, just do 39 divided by 7.
00:08:26.200 --> 00:08:34.200
39 inside; divided by 7; put the decimal point at the end; bring it up.
00:08:34.200 --> 00:08:38.200
I can add a 0 there if I want; I can add two 0s.
00:08:38.200 --> 00:08:40.500
I can add three; it doesn't matter.
00:08:40.500 --> 00:08:48.400
7 fits into 39 five times; that is 35; subtract it; I get 4.
00:08:48.400 --> 00:08:58.200
Bring down this 0; 7 goes into 40 again five times; that is 35.
00:08:58.200 --> 00:09:04.500
Subtract it; I get 5; I can bring down another 0.
00:09:04.500 --> 00:09:11.800
7 goes into 50 seven times; that is 49.
00:09:11.800 --> 00:09:16.000
Usually as long as you have one or two numbers behind the decimal point,
00:09:16.000 --> 00:09:19.500
you can probably just stop there and write that as your answer.
00:09:19.500 --> 00:09:26.000
Maybe like 5.57 or 5 point and then what you can do is maybe you can round this number.
00:09:26.000 --> 00:09:31.600
This number is 5 or greater.
00:09:31.600 --> 00:09:37.800
What you can do is you can round this number up to be 5.6.
00:09:37.800 --> 00:09:44.700
That is the mean; I am just going to write 5.6.
00:09:44.700 --> 00:09:48.100
Either one will be your answer.
00:09:48.100 --> 00:09:55.400
The next one, median; remember the median, the keyword is middle.
00:09:55.400 --> 00:09:59.000
Be careful here, the most common mistake for this one
00:09:59.000 --> 00:10:04.900
is just finding the middle number from your data set.
00:10:04.900 --> 00:10:09.600
Make sure you have to write the number in order from least to greatest.
00:10:09.600 --> 00:10:16.400
My smallest number here I see is 3; I have another 3.
00:10:16.400 --> 00:10:28.200
I have this is 4, then 5, 6, 8, and 10.
00:10:28.200 --> 00:10:31.800
Make sure I have one, two, three, four, five, six, seven numbers.
00:10:31.800 --> 00:10:39.000
The number in the middle, I can cross out the outside numbers one more time.
00:10:39.000 --> 00:10:45.200
My median will be 5.
00:10:45.200 --> 00:10:51.700
The last one, the mode is most; the mode is most.
00:10:51.700 --> 00:10:56.900
What number do you see the most?--what number occurs the most?
00:10:56.900 --> 00:11:02.600
That would be the 3 because 3 you see it twice.
00:11:02.600 --> 00:11:14.100
The other numbers, you only see them once; 3 is going to be the mode.
00:11:14.100 --> 00:11:17.400
The next example, same thing.
00:11:17.400 --> 00:11:23.000
Find the mean, median, mode for the following set of data.
00:11:23.000 --> 00:11:32.400
We have four numbers here for the mean; this is average.
00:11:32.400 --> 00:11:36.400
We are going to add up all the numbers divided by however many numbers we have.
00:11:36.400 --> 00:11:43.300
It is 15 plus 12 plus 19 and plus 10.
00:11:43.300 --> 00:11:48.200
Divide that by... I have four numbers.
00:11:48.200 --> 00:11:55.400
15 plus 12 is 27; write that there.
00:11:55.400 --> 00:12:02.300
27 plus 19... 7 plus 9 is 16; bring up the 1.
00:12:02.300 --> 00:12:07.300
I am going to write that 6 right here; 2, 3, 4.
00:12:07.300 --> 00:12:14.200
27 plus 19 is 46; add the 10; you are going to get 56.
00:12:14.200 --> 00:12:27.700
Divide that by 4; 56 and 4; I want to just divide it.
00:12:27.700 --> 00:12:34.100
56 is going to go on the inside for 56 divided by 4.
00:12:34.100 --> 00:12:41.900
4 goes into 5 one time; that gives you 4; subtract it.
00:12:41.900 --> 00:12:45.600
Get 1 left over; bring down this number, 6.
00:12:45.600 --> 00:12:57.000
4 goes into 16 four times; my mean is 14.
00:12:57.000 --> 00:13:04.200
My median, that your middle number.
00:13:04.200 --> 00:13:07.300
Let's write our numbers in order from least to greatest.
00:13:07.300 --> 00:13:24.800
That is 12, then... forgot the 10; 10, 12, 15, 19.
00:13:24.800 --> 00:13:30.800
The middle number, we have two middle numbers.
00:13:30.800 --> 00:13:35.000
We are looking for the middle right in between 12 and 15.
00:13:35.000 --> 00:13:38.700
We are going to find the average; we can add those two numbers together.
00:13:38.700 --> 00:13:49.700
It is 12 plus 15 divided by 2; this becomes 27 divided by 2.
00:13:49.700 --> 00:13:55.200
We can again change it to a decimal or leave it as a fraction.
00:13:55.200 --> 00:14:00.600
27... I don't know why I wrote that.
00:14:00.600 --> 00:14:09.600
27 divided by 2; 2 goes into 2, this first number, one time.
00:14:09.600 --> 00:14:14.300
That is 2; subtract it; get 0; bring down the 7.
00:14:14.300 --> 00:14:23.300
2 goes into 7 three times which is a 6; subtract it; get a 1.
00:14:23.300 --> 00:14:27.500
From here, since I have a remainder, I can just go ahead and add my decimal point.
00:14:27.500 --> 00:14:32.400
Bring it up; add the 0; bring down the 0.
00:14:32.400 --> 00:14:40.700
2 goes into 10 five times; that gives me 10; I get no remainders.
00:14:40.700 --> 00:14:50.600
My median here is going to be 13.5.
00:14:50.600 --> 00:15:00.500
The last one is mode; the mode is the number that occurs the most.
00:15:00.500 --> 00:15:06.000
15, we only see it once; 12 only once; 19 once; 10 once.
00:15:06.000 --> 00:15:13.600
For the mode, we have none; we can just write none.
00:15:13.600 --> 00:15:23.100
The next example, Sarah's test scores for the last five chapters are 90, 92, 86, 97, and 90.
00:15:23.100 --> 00:15:31.200
Find the mode, mean, and median of her scores; let's start with the mode.
00:15:31.200 --> 00:15:39.000
The mode, keyword most; we look at what number occurs the most.
00:15:39.000 --> 00:15:48.800
The 90, we see 90 twice; my mode is going to be 90.
00:15:48.800 --> 00:15:59.200
The next one is mean; mean is the average.
00:15:59.200 --> 00:16:01.000
We are going to add up all the numbers.
00:16:01.000 --> 00:16:21.400
90 plus 92 plus 86 plus 97 plus 90; all over... 1, 2, 3, 4, 5... 5.
00:16:21.400 --> 00:16:30.800
Let's do this one right here; 90 plus 92 is... 2 and then 18.
00:16:30.800 --> 00:16:34.800
Then I am going to add the next number, 86; plus 86.
00:16:34.800 --> 00:16:35.600
You can do it this way.
00:16:35.600 --> 00:16:41.100
Or you can just maybe list them all out and then add them up like that.
00:16:41.100 --> 00:16:50.800
86; this is 8; 8 plus 8 is 16; that is 2.
00:16:50.800 --> 00:16:56.900
We got this, this, this; now we have to add 97.
00:16:56.900 --> 00:17:07.900
That is 15; this is 1 plus 9 is 10; plus 6 is 16; this is 3.
00:17:07.900 --> 00:17:20.400
The last one, 90; this is 5; this is 15; this is 4.
00:17:20.400 --> 00:17:28.300
When I add up all the numbers, it becomes 455.
00:17:28.300 --> 00:17:31.700
Divided by... I have five numbers.
00:17:31.700 --> 00:17:37.200
I know that 5 is going to go into this number evenly because it ends in a 5.
00:17:37.200 --> 00:17:42.900
The number ends in a 5 or 0, then it is going to be divisible by 5.
00:17:42.900 --> 00:17:55.900
455, let's divide it; 5 doesn't go into 4; 5 goes into 45 nine times.
00:17:55.900 --> 00:18:00.000
That is going to give you 45; subtract it; get a 0.
00:18:00.000 --> 00:18:10.000
Bring down the 5; 5 goes into 5 one time; that is a 5.
00:18:10.000 --> 00:18:19.200
My answer is 91; that is my mean, the average; mean.
00:18:19.200 --> 00:18:26.300
That means her test scores, if she scored these scores, her average is 91.
00:18:26.300 --> 00:18:32.500
She is averaging pretty well; that is an A.
00:18:32.500 --> 00:18:40.000
The last one is the median which is the middle.
00:18:40.000 --> 00:18:45.500
The middle number, let's list our numbers in order from least to greatest.
00:18:45.500 --> 00:18:50.100
The smallest number is 86.
00:18:50.100 --> 00:19:04.100
Then we have 90; then 90 again; 92; and then 97.
00:19:04.100 --> 00:19:13.200
Our median, our middle number, is 90.
00:19:13.200 --> 00:19:23.800
The fourth example, the daily temperature for the last few days were 72, 70, 83, 75, 81, and 75.
00:19:23.800 --> 00:19:26.300
Find the three measures of central tendency.
00:19:26.300 --> 00:19:40.200
We have the mean, the median, then we have the mode.
00:19:40.200 --> 00:19:43.700
First, mean; we know the keyword for the mean is average.
00:19:43.700 --> 00:19:50.100
We have to add up all the numbers and divide it by however many numbers we have.
00:19:50.100 --> 00:19:54.600
That is 70... 72 is our first one.
00:19:54.600 --> 00:20:10.700
72 plus 70 plus 83 plus 75 plus 81 plus 75.
00:20:10.700 --> 00:20:14.300
I have one, two, three, four, five, six numbers.
00:20:14.300 --> 00:20:22.300
I am going to divide this sum by 6 because I have six numbers.
00:20:22.300 --> 00:20:28.100
Let's add up the numbers; 72 plus 70.
00:20:28.100 --> 00:20:31.800
I am just going to add up just like how I did before.
00:20:31.800 --> 00:20:38.200
2 plus 0 is 2; this is 14; I am going to take this number.
00:20:38.200 --> 00:20:44.200
I got this; I got that one; add this number, 83.
00:20:44.200 --> 00:20:51.500
This is 5; this is 12; and then 2.
00:20:51.500 --> 00:21:03.400
Add the 75; this is 10; 7; 9; 10; this is 3.
00:21:03.400 --> 00:21:11.400
Add this one, 81; 1; 8; 3.
00:21:11.400 --> 00:21:18.300
The last one is 75; this is 6.
00:21:18.300 --> 00:21:34.000
8 plus 7 is 15; 3 plus 1 is 4; 456; 456 divided by 6.
00:21:34.000 --> 00:21:48.500
Let's divide this number by 6; 56 divided by 6.
00:21:48.500 --> 00:21:51.500
I know that 6 cannot fit into 4.
00:21:51.500 --> 00:21:55.900
6 is going to fit into 45, this number here.
00:21:55.900 --> 00:22:01.400
6, let's see; 6 times 6 is 36; 6 times 7 is 42.
00:22:01.400 --> 00:22:07.800
6 times 8 is 48; we know that it is 7; this is 42.
00:22:07.800 --> 00:22:13.200
If I subtract it, I get 3; bring down this number here, 6.
00:22:13.200 --> 00:22:20.300
6 goes into 36 six times; that is 36; 0.
00:22:20.300 --> 00:22:31.300
My mean here is 76; that is the average.
00:22:31.300 --> 00:22:36.000
Let me just write this a little bit lower.
00:22:36.000 --> 00:22:46.200
The next one is median; median, we know the keyword is middle.
00:22:46.200 --> 00:22:53.000
We are going to look for the middle number after we list the numbers out in order from least to greatest.
00:22:53.000 --> 00:23:04.300
The smallest number is 70; then let's see, 72.
00:23:04.300 --> 00:23:20.800
Then 75; then again 75; then 81; and 83.
00:23:20.800 --> 00:23:26.400
I have my six numbers; the middle number now.
00:23:26.400 --> 00:23:31.100
I am going to cross out the last numbers; cross those out.
00:23:31.100 --> 00:23:34.300
Then I have two numbers here.
00:23:34.300 --> 00:23:39.300
Normally when you have two numbers, you are going to have to find the average between those two numbers.
00:23:39.300 --> 00:23:43.000
You are going to have to find the middle number between those two.
00:23:43.000 --> 00:23:45.600
You would add them; divided by 2.
00:23:45.600 --> 00:23:56.100
But I know since they are both 75, the number in the middle of 75 will just be 75.
00:23:56.100 --> 00:23:59.200
Median will just be 75.
00:23:59.200 --> 00:24:05.700
It is the same number so then our median has to be that same number.
00:24:05.700 --> 00:24:11.600
The last one, the mode, the keyword here is most.
00:24:11.600 --> 00:24:18.000
What number from all the six numbers on our data, what number do we see the most?
00:24:18.000 --> 00:24:24.100
That number would be 75.
00:24:24.100 --> 00:24:30.000
It is the number that occurs the most; that is 75.
00:24:30.000 --> 00:24:32.000
That is it for this lesson; thank you for watching Educator.com.