Basic Math Measures of Central Tendency

Welcome back to Educator.com.0000

For the next lesson, we are going to go over measures of central tendency.0002

The measures of central tendency are just three different types of ways you can describe data.0008

If you have a set of numbers, if you have some numbers,0018

then there are three ways you can represent the measures of those numbers.0022

The first one, the first measure of central tendency is the mean.0031

The mean is the sum of all the numbers divided by however many numbers you have.0035

Another word for it is average.0043

You are looking for the average of all the numbers in your data.0044

The next one is median.0049

Median is when you list out all the numbers in order from least to greatest,0051

you are going to find the middle number, the one that is right in the middle.0058

That is called the median; the key word here is middle.0062

The third one is the mode; the mode is the number that occurs the most.0067

It is the number that you see the most in your set of data.0072

The keyword here is going to be most.0075

Let's say if I have a set of numbers, let's say 1, 2, 3, 4, and 5.0080

The mean, keyword average, we are going to find the average of all those numbers.0087

We are going to add them all up; 1 plus 2 plus 3 plus 4 plus 5.0095

You are going to divide by however many numbers you have.0102

Here we have five different numbers; you are going to divide that sum by 5.0107

1 plus 2 is 3.0115

I am just going to write that number on top like that.0118

That is 3 plus 3 is 6; 6 plus 4 is 10; 10 plus 5 is 15.0122

This looks like a fraction... if I write it like... I am sorry; wrote the wrong number.0130

5... if write it like that, it looks like a fraction.0138

But fractions are division; you can just think of that as 15 divided by 5.0141

15 divided by 5; we know that 5 goes into 15 three times.0148

15 divided by 5 is 3; the mean is 3.0154

That is the average of those five numbers.0160

The median of that set of data is going to the middle number0164

but only when you list it out in order from least to greatest.0170

You must list it out.0174

Here it is already listed from least to greatest; 1, 2, 3, 4, 5.0177

The number in the middle will be this number right there; the median is 3.0184

When you have two numbers in the middle, let's say you have an even number of numbers.0196

Say it is just 1, 2, 3, and 4.0202

If that is your data, you have two numbers in the middle.0207

Then you are going to find the average between those two numbers.0212

We are going to add those two numbers and divide it by 2.0216

That will be 2 plus 3 divided by... there is only two numbers there so it is 2.0220

That is going to be 5/2.0227

You can usually leave it as a fraction.0231

If you want, you can change it to a mixed number.0234

How many times does 2 fit into 5?--2 fits into 5 two times.0236

You have 1 left over; keep your same denominator.0243

That is how you change... this is called an improper fraction0248

when the number on the top is bigger than the number on the bottom.0251

You can change it to a mixed number where you are going to have a whole number and then a proper fraction.0255

Again 2 fits into 5 two times; that becomes your whole number, 2.0263

Your leftovers is 1 over... your denominator is 2.0267

You can leave it like that.0271

Or if you want, you can just do 5 divided by 2, and change it to a decimal.0273

Remember 5, this top number, goes inside; that is on the outside.0283

Put a decimal point at the end of that number; bring it up.0290

2 fits into 5 twice; that is a 4; we subtract; get 1.0293

I can add 0s there at the end of that number behind the decimal point.0301

Bring that 0 down; 2 goes into 10 five times.0307

That is 10; my remainder is 0.0314

Your median here, when we find the average of that, will either be 2 and 1/2 or 2.5.0318

You could just think of it as halfway between 2 and 3.0330

That is the average; between 2 and 3 is going to be 2 and 1/2; 2.5.0334

The third one, the mode, remember the keyword here is most.0342

It is the one that you see the most.0346

Here with our set of data, 1, 2, 3, 4, 5, you only see each of the numbers one time.0350

In this case, we have no mode.0359

If you had 1, 2, 2, and 3, then you know the mode would be 2 because you see that number the most.0363

It occurs the most; that is the mode.0373

Again mean is average; median is middle; mode is most.0377

First example, using this set of data, we are going to find the mean, median, and mode.0386

Mean, we are just going to add up all the numbers.0393

For mean, it doesn't if the numbers are in order because when you add, the order doesn't matter.0397

If I add 1 plus 2, it is going to be the same thing as 2 plus 1.0403

Here just add up all the numbers; 3 plus 5 plus 3 plus 8 plus 6 plus 10 plus 4.0407

Then we are going to divide that number by 1, 2, 3, 4, 5, 6, 7, seven numbers.0420

3 plus 5 is 8; plus 3 is 11.0431

That is 19; that is 25; that is 35; that is 39.0436

It is going to be 39; that is the sum; divided by 7.0444

You can either leave it like this as long as it doesn't simplify.0453

As long as there is no factors that goes into 39 and 7, you can just leave it as an improper fraction.0456

To change it to a mixed number, we ask ourselves how many times does 7 fit into 39?0467

I know 7 times 5 is 35; 7 times 6 is 42; that is too big.0474

My whole number is going to be 5 because 7 fits into 39 five times.0481

I have 4 leftovers; 4 over... keep the same denominator.0487

That will be our mean.0495

Again if you want to change this to a decimal instead, just do 39 divided by 7.0499

39 inside; divided by 7; put the decimal point at the end; bring it up.0506

I can add a 0 there if I want; I can add two 0s.0514

I can add three; it doesn't matter.0518

7 fits into 39 five times; that is 35; subtract it; I get 4.0520

Bring down this 0; 7 goes into 40 again five times; that is 35.0528

Subtract it; I get 5; I can bring down another 0.0538

7 goes into 50 seven times; that is 49.0544

Usually as long as you have one or two numbers behind the decimal point,0552

you can probably just stop there and write that as your answer.0556

Maybe like 5.57 or 5 point and then what you can do is maybe you can round this number.0559

This number is 5 or greater.0566

What you can do is you can round this number up to be 5.6.0571

That is the mean; I am just going to write 5.6.0578

Either one will be your answer.0585

The next one, median; remember the median, the keyword is middle.0588

Be careful here, the most common mistake for this one0595

is just finding the middle number from your data set.0599

Make sure you have to write the number in order from least to greatest.0605

My smallest number here I see is 3; I have another 3.0609

I have this is 4, then 5, 6, 8, and 10.0616

Make sure I have one, two, three, four, five, six, seven numbers.0628

The number in the middle, I can cross out the outside numbers one more time.0632

My median will be 5.0639

The last one, the mode is most; the mode is most.0645

What number do you see the most?--what number occurs the most?0652

That would be the 3 because 3 you see it twice.0657

The other numbers, you only see them once; 3 is going to be the mode.0662

The next example, same thing.0674

Find the mean, median, mode for the following set of data.0677

We have four numbers here for the mean; this is average.0683

We are going to add up all the numbers divided by however many numbers we have.0692

It is 15 plus 12 plus 19 and plus 10.0696

Divide that by... I have four numbers.0703

15 plus 12 is 27; write that there.0708

27 plus 19... 7 plus 9 is 16; bring up the 1.0715

I am going to write that 6 right here; 2, 3, 4.0722

27 plus 19 is 46; add the 10; you are going to get 56.0727

Divide that by 4; 56 and 4; I want to just divide it.0734

56 is going to go on the inside for 56 divided by 4.0748

4 goes into 5 one time; that gives you 4; subtract it.0754

Get 1 left over; bring down this number, 6.0762

4 goes into 16 four times; my mean is 14.0765

My median, that your middle number.0777

Let's write our numbers in order from least to greatest.0784

That is 12, then... forgot the 10; 10, 12, 15, 19.0787

The middle number, we have two middle numbers.0805

We are looking for the middle right in between 12 and 15.0811

We are going to find the average; we can add those two numbers together.0815

It is 12 plus 15 divided by 2; this becomes 27 divided by 2.0819

We can again change it to a decimal or leave it as a fraction.0830

27... I don't know why I wrote that.0835

27 divided by 2; 2 goes into 2, this first number, one time.0840

That is 2; subtract it; get 0; bring down the 7.0849

2 goes into 7 three times which is a 6; subtract it; get a 1.0854

From here, since I have a remainder, I can just go ahead and add my decimal point.0863

Bring it up; add the 0; bring down the 0.0867

2 goes into 10 five times; that gives me 10; I get no remainders.0872

My median here is going to be 13.5.0881

The last one is mode; the mode is the number that occurs the most.0890

15, we only see it once; 12 only once; 19 once; 10 once.0900

For the mode, we have none; we can just write none.0906

The next example, Sarah's test scores for the last five chapters are 90, 92, 86, 97, and 90.0913

Find the mode, mean, and median of her scores; let's start with the mode.0923

The mode, keyword most; we look at what number occurs the most.0931

The 90, we see 90 twice; my mode is going to be 90.0939

The next one is mean; mean is the average.0949

We are going to add up all the numbers.0959

90 plus 92 plus 86 plus 97 plus 90; all over... 1, 2, 3, 4, 5... 5.0961

Let's do this one right here; 90 plus 92 is... 2 and then 18.0981

Then I am going to add the next number, 86; plus 86.0991

You can do it this way.0995

Or you can just maybe list them all out and then add them up like that.0995

86; this is 8; 8 plus 8 is 16; that is 2.1001

We got this, this, this; now we have to add 97.1011

That is 15; this is 1 plus 9 is 10; plus 6 is 16; this is 3.1017

The last one, 90; this is 5; this is 15; this is 4.1028

When I add up all the numbers, it becomes 455.1040

Divided by... I have five numbers.1048

I know that 5 is going to go into this number evenly because it ends in a 5.1052

The number ends in a 5 or 0, then it is going to be divisible by 5.1057

455, let's divide it; 5 doesn't go into 4; 5 goes into 45 nine times.1063

That is going to give you 45; subtract it; get a 0.1076

Bring down the 5; 5 goes into 5 one time; that is a 5.1080

My answer is 91; that is my mean, the average; mean.1090

That means her test scores, if she scored these scores, her average is 91.1099

She is averaging pretty well; that is an A.1106

The last one is the median which is the middle.1112

The middle number, let's list our numbers in order from least to greatest.1120

The smallest number is 86.1125

Then we have 90; then 90 again; 92; and then 97.1130

Our median, our middle number, is 90.1144

The fourth example, the daily temperature for the last few days were 72, 70, 83, 75, 81, and 75.1153

Find the three measures of central tendency.1164

We have the mean, the median, then we have the mode.1166

First, mean; we know the keyword for the mean is average.1180

We have to add up all the numbers and divide it by however many numbers we have.1184

That is 70... 72 is our first one.1190

72 plus 70 plus 83 plus 75 plus 81 plus 75.1194

I have one, two, three, four, five, six numbers.1211

I am going to divide this sum by 6 because I have six numbers.1214

Let's add up the numbers; 72 plus 70.1222

I am just going to add up just like how I did before.1228

2 plus 0 is 2; this is 14; I am going to take this number.1232

I got this; I got that one; add this number, 83.1238

This is 5; this is 12; and then 2.1244

Add the 75; this is 10; 7; 9; 10; this is 3.1251

Add this one, 81; 1; 8; 3.1263

The last one is 75; this is 6.1271

8 plus 7 is 15; 3 plus 1 is 4; 456; 456 divided by 6.1278

Let's divide this number by 6; 56 divided by 6.1294

I know that 6 cannot fit into 4.1308

6 is going to fit into 45, this number here.1311

6, let's see; 6 times 6 is 36; 6 times 7 is 42.1316

6 times 8 is 48; we know that it is 7; this is 42.1321

If I subtract it, I get 3; bring down this number here, 6.1328

6 goes into 36 six times; that is 36; 0.1333

My mean here is 76; that is the average.1340

Let me just write this a little bit lower.1351

The next one is median; median, we know the keyword is middle.1356

We are going to look for the middle number after we list the numbers out in order from least to greatest.1366

The smallest number is 70; then let's see, 72.1373

Then 75; then again 75; then 81; and 83.1384

I have my six numbers; the middle number now.1401

I am going to cross out the last numbers; cross those out.1406

Then I have two numbers here.1411

Normally when you have two numbers, you are going to have to find the average between those two numbers.1414

You are going to have to find the middle number between those two.1419

You would add them; divided by 2.1423

But I know since they are both 75, the number in the middle of 75 will just be 75.1425

Median will just be 75.1436

It is the same number so then our median has to be that same number.1439

The last one, the mode, the keyword here is most.1446

What number from all the six numbers on our data, what number do we see the most?1451

That number would be 75.1458

It is the number that occurs the most; that is 75.1464

That is it for this lesson; thank you for watching Educator.com.1470