For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Measures of Central Tendency

#### Related Links

- The three measures of central tendency help describe a set of data
- Mean is the sum of the numbers divided by the number of addends (average)
- Median is the middle number when arranged in numerical order (middle)
- Mode is the number that occurs most often (most)

### Measures of Central Tendency

(15,25,5,10,20)

- Mean: [(15 + 25 + 5 + 10 + 20)/5] = [75/5] = 15
- Median: 5,10,
__15__,20,25 - Mode: None

(15,25,5,11)

- Mean: [(15 + 25 + 5 + 11)/4] = [56/4] = 14
- Median: 5,
__11__,__15__,25 = [(11 + 15)/2] = 13 - Mode: None

(5,25,5,13)

- Mean: [(5 + 25 + 5 + 13)/4] = [48/4] = 12
- Median: 5,
__5__,__13__,25 = [(5 + 13)/2] = 9 - Mode: 5

(3,2,3,3,4)

- Mean: [(3 + 2 + 3 + 3 + 4)/5] = [15/5] = 3
- Median: 2,3,
__3__,3,4 - Mode: 3

(4,4,4,2,6)

- Mean: [(4 + 4 + 4 + 2 + 6)/5] = [20/5] = 4
- Median: 2,4,
__4__,4,6 - Mode: 4

- Mean: [(50 + 100 + 85 + 95 + 90)/5] = [420/5] = 84
- Median: 50,85,
__90__,95,100 - Mode: None

- Mean: [(100 + 100 + 85 + 95 + 90)/5] = [470/5] = 94
- Median: 85,90,
__95__,100,100 - Mode: 100

- Mean: [(100 + 85 + 95 + 92)/4] = [372/4] = 93
- Median: 85,
__92__,__95__,100 = [(92 + 95)/2] = 93.5 - Mode: None

- Mean: [(45 + 16 + 32 + 16 + 12 + 17)/6] = [138/6] = 29
- Median: 12,16,
__16__,__17__,32,45 = [(16 + 17)/2] = 16.5 - Mode: 16

- Mean: [(72 + 96 + 72 + 75 + 80)/5] = [395/5] = 79
- Median: 72,72,
__75__,80,96 = 75 - Mode: 72

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Measures of Central Tendency

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Measures of Central Tendency
- Extra Example 1: Find the Mean, Median, and Mode for the Following Set of Data
- Extra Example 2: Find the Mean, Median, and Mode for the Following Set of Data
- Extra Example 3: Find the Mean, Median, and Mode for the Following Set of Data
- Extra Example 4: Find the Three Measures of the Central Tendency

- Intro 0:00
- Measures of Central Tendency 0:06
- Mean
- Median
- Mode
- Extra Example 1: Find the Mean, Median, and Mode for the Following Set of Data 6:24
- Extra Example 2: Find the Mean, Median, and Mode for the Following Set of Data 11:14
- Extra Example 3: Find the Mean, Median, and Mode for the Following Set of Data 15:13
- Extra Example 4: Find the Three Measures of the Central Tendency 19:12

### Basic Math Online Course

### Transcription: 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 number*0164

*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 fraction*0248

*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 one*0595

*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

0 answers

Post by Milan Ray on April 15, 2014

This is hard even I already know this

3 answers

Last reply by: Lucas Santiago

Sun Jul 15, 2012 5:42 PM

Post by Samvel Karapetyan on May 11, 2012

What if the mode is 1,2,2,3,3,4....?