Math Antics - Mean, Median and Mode - Free Educational videos for Students in K-12

Math Antics - Mean, Median and Mode - By Mathantics

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00:03	Uh huh . Hi , this is rob . Welcome
00:07	to Math Antics . In this lesson we're going to
00:09	learn about three important math concepts called the mean the
00:12	median and the mode math often deals with datasets and
00:16	data sets are often just collections or groups of numbers
00:20	. These numbers may be the results of scientific measurements
00:23	or surveys or other data collection methods . For example
00:27	, you might record the ages of each member of
00:29	your family into a data set or you might measure
00:32	the weight of each of your pets unless them in
00:34	a dataset . Those data sets are fairly small and
00:37	easy to understand . But you could have much bigger
00:40	datasets . A really big data set might contain the
00:42	cost of every item in a store or the top
00:45	speed of every land mammal or the brightness of all
00:48	the stars in our galaxy . Those data sets will
00:51	contain a lot of different numbers . And if you
00:54	have to look at a big data set all at
00:55	one time it would be pretty hard to make sense
00:58	of it or say much about it besides , well
01:00	that's a lot of numbers but that's where mean ,
01:03	median and mode can really help us out . There
01:06	are three different properties a data sets that can give
01:09	us useful . Easy to understand information about the data
01:11	set so that we can see the big picture and
01:14	understand what the data means about the world we live
01:16	in . That sounds pretty useful . Huh ? So
01:19	let's learn what each property really is and find out
01:21	how to calculate them for any particular dataset . Let's
01:25	start with the mean . You may not have ever
01:27	heard of something called the mean before but I'll bet
01:30	you've heard of the average . If so then I've
01:33	got good news . Mean means average mean an average
01:37	are just two different terms for the exact same property
01:39	of a data set . The mean or average is
01:42	an extremely useful property to understand what it is .
01:45	Let's look at a simple data set that contains five
01:47	numbers as a visual aid . Let's also represent those
01:50	numbers with stacks of blocks whose heights correspond to their
01:53	values 183 to 6 . Right now , since each
01:58	of the five numbers is different , the stacks of
02:01	blocks are all different heights . But what if we
02:03	rearrange the blocks with the goal of making the stacks
02:06	of the same height ? In other words , if
02:08	each stack could have the exact same amount , what
02:10	would that amount be ? Well with a bit of
02:13	trial and error ? You'll see that we have enough
02:14	blocks for each stack to have a total of four
02:17	. That means that the mean or average for original
02:20	Dataset would be four . Some of the numbers are
02:23	greater than four and some are less . But if
02:25	the amounts could all be made the same , they
02:27	would all become for . So that's the concept of
02:30	the mean . It's the value you'd get if you
02:32	could smooth out or flatten all of the different data
02:35	values into one consistent value . But is there a
02:39	way that we could use math to calculate the mean
02:41	of a dataset ? After all ? It would be
02:43	very inconvenient if we always had to use stacks of
02:46	blocks to do it . There's gotta be an easier
02:49	way man . It's tough . Yeah . To learn
02:55	the mathematical procedure for calculating the mean . Let's start
02:58	with blocks again . But this time instead of using
03:00	trial and error , let's use a more systematic way
03:02	to make the stacks all the same height . This
03:05	way involves a clever combination of addition and division .
03:09	We know that we want to end up with five
03:10	stacks that all have the same number of blocks .
03:12	Right ? So first let's add up all of the
03:15	numbers , which is like putting all of the blocks
03:17	we have into one big stack , Adding up all
03:20	of the numbers , or counting all the blocks shows
03:22	us that we have a total of 20 . Next
03:25	we divide that number or stack into five equal parts
03:28	. Since the stack has a total of 20 blocks
03:31	, dividing it into five equal stacks means that we'll
03:33	have four in each since 20 divided by five equals
03:36	four . So that's the math procedure you use to
03:39	find the mean of a data set . It's just
03:41	two simple steps . First , you add up all
03:44	the numbers in the set and then you divide the
03:46	total you get by how many numbers you add it
03:48	up . The answer you get is the mean of
03:51	the data set . Let's use that procedure to find
03:54	the mean age of the members of this fine looking
03:56	family here . If we add them all up using
03:58	a calculator or by hand , if you'd like ,
04:00	the total of the ages is 222 years . But
04:04	then we need to divide that total by the number
04:06	of ages we added , which is six , 222
04:09	, divided by six is 37 . So that's the
04:12	mean age of all the members in this family .
04:15	All right . That's the mean . Now what about
04:18	the median ? The median is the middle of a
04:20	dataset ? It's the number that splits the data set
04:23	into two equally sized groups or halves . One half
04:26	contains members that are greater than or equal to the
04:28	median and the other half contains members that are less
04:31	than or equal to the median . Sometimes finding the
04:34	median of a data set is easy and sometimes it's
04:36	hard . That's because finding the middle value of a
04:39	dataset requires that its members be an order from the
04:42	least to the greatest or vice versa . And if
04:46	the data set has a lot of numbers , it
04:47	might take a lot of work to put them in
04:49	the right order if they aren't already that way .
04:52	So to make things easier , let's start with a
04:54	really basic data set that isn't in order . It's
04:57	pretty easy to see that we can put this data
04:59	set in order from the least to the greatest value
05:01	just by switching the two in the one there .
05:04	Now we have the data set 123 And finding the
05:07	median or middle of this data set is easy .
05:10	It's just too because the two is located exactly in
05:13	the middle . That almost seems too easy , doesn't
05:15	it ? But don't worry , it gets harder .
05:17	But before we try a harder problem , I want
05:19	to point out that sometimes the mean and the median
05:22	of a data set are the same number and sometimes
05:24	they're not in the case of our simple data set
05:27	123 the meeting is to And the mean is also
05:30	too . As you can see if we rearrange the
05:32	amounts or follow the procedure , we learn to calculate
05:35	the mean . But what about the first data set
05:37	that we found ? The mean of ? We determined
05:39	that the mean of this data set is for .
05:41	But what about the median ? Well , the median
05:44	is the middle . And since this data set is
05:47	already in order from least to greatest , It's easy
05:49	to see that the three is located in the middle
05:52	since it splits the other members into two equal groups
05:55	. So for this data set , the mean is
05:57	four , but the median is three . So to
06:00	find the median of a set of numbers first ,
06:02	you need to make sure that all the numbers are
06:04	in order . And then you can identify the member
06:06	that's exactly in the middle by making sure there's an
06:09	equal number of members on either side of it .
06:11	Okay . So far so good . But some of
06:14	you may be wondering what if a dataset doesn't have
06:17	an obvious middle member ? All of the sets we
06:19	found the median of so far have an odd number
06:21	of members . But what if a set has an
06:24	even number of members like the data set ? 1234
06:28	There isn't a member in the middle that splits the
06:30	set into two equally sized groups . If that's the
06:33	case , we can actually use what we learned about
06:35	the mean . To help us out . If the
06:37	dataset has an even number of members , then to
06:40	find the median , we need to take the middle
06:42	two numbers and calculate the mean or average of those
06:45	two . By doing that , we're basically figuring out
06:48	what number would be exactly halfway between the two middle
06:51	numbers and that number will be our medium . For
06:55	example , in the set 1234 we need to take
06:58	the middle two numbers two and three and find the
07:00	mean of those numbers . We can do that by
07:03	adding two and three and then dividing by two ,
07:06	two plus two equals five and five divided by two
07:08	is 2.5 . So the median of the data set
07:11	is 2.5 . Even though the number 2.5 isn't actually
07:16	a member of the data set , it's the median
07:18	because it represents the middle of the data set and
07:21	it splits the members into two equally sized groups .
07:24	Okay , so now , you know the difference between
07:26	mean and median ? But what about the mode of
07:29	a data set ? What in the world does that
07:31	mean ? Well , mode is just a technical word
07:35	for the value in a data set that occurs most
07:37	often in the datasets . We've seen so far .
07:40	There hasn't even been a mode because none of the
07:42	data values were ever repeated . But what if you
07:45	had this data set ? This set has six members
07:48	, but some of the values are repeated . If
07:50	we rearrange them , you can see that there's 112
07:53	twos and three threes . The mode of this data
07:56	set is the value that occurs most often or most
07:59	frequently . So that would be three . Since there's
08:02	three threes Now don't get confused just because the #
08:05	three was repeated three times . The mod is the
08:08	number that's repeated most often ? Not how many times
08:11	it was repeated as I mentioned . If each member
08:14	in the dataset occurs only once . It has no
08:16	mode . But it's also possible for a data set
08:18	to have more than one mode . Here is an
08:20	example of a data set like that . In this
08:23	set , the number seven is repeated twice , but
08:25	so is the number 15 . That means they tie
08:28	for the title of mode . This set has two
08:30	modes , seven and 15 . Okay , So now
08:34	that you know what the mean , median and mode
08:36	of a data set are let's put all that new
08:38	information to use in one final real world example ,
08:42	suppose there's this guy who makes and sells custom electric
08:45	guitars . Here is a table showing how many guitars
08:48	he sold during each month of the year . Let's
08:51	find the mean median and mode of this data set
08:54	. First to find the mean . We need to
08:56	add up the number of guitar sold in each month
08:59	. You can do the addition by hand or you
09:00	can use a calculator if you want to . Either
09:02	way , be careful since that's a lot of numbers
09:05	stand up and we don't want to make a mistake
09:07	. The answer I get is 108 . So that's
09:10	the total he sold for the whole year . But
09:12	to get the mean sold each month , we need
09:14	to divide that total by the number of months ,
09:16	which is 12 108 , divided by 12 is nine
09:20	. So the mean or average is nine Next to
09:24	find the median of the data set . We're going
09:25	to have to rearrange the 12 data points in order
09:28	from smallest to largest . So we can figure out
09:30	what the middle value is there . That's better .
09:34	Since there's an even number of members in this set
09:36	, we can't just choose the middle number . So
09:38	we're going to have to pick the Middle two numbers
09:40	and then find the mean of them . nine and
09:42	10 are in the middle . Since there's an equal
09:44	number of data values on either side of them .
09:46	So we need to take the mean of nine and
09:48	10 . That's easy . Nine plus 10 equals 19
09:52	and then 19 divided by two is 9.5 . So
09:55	the median number of guitar sold is 9.5 . That
09:59	means that in half of the months he sold more
10:00	than 9.5 and in half of the months he sold
10:03	less than 9.5 . Last of all , let's identify
10:06	the mode of this data set if there is one
10:09	. Well , let's see there's two eights in the
10:11	dataset . Oh , but there's 3/10 That looks like
10:15	the most frequent number . So 10 is the mode
10:18	of this data set . It's the result that occurred
10:20	most often . All right . So that's the basics
10:23	of mean median and mode . There are three really
10:27	useful properties of datasets and now you know how to
10:29	find them . But sometimes the hardest part about mean
10:33	median and mode is just remembering which is which So
10:36	remember that mean means average median is in the middle
10:41	and mode starts with M . O . Which can
10:43	remind you that it's the number that occurs most often
10:47	. Remember to get good at Math . You need
10:49	to do more than just watch videos about it .
10:51	You need to practice so be sure to try finding
10:53	the mean median and mode on your own . As
10:56	always . Thanks for watching Math Antics and I'll see
10:58	you next time . Learn more at Math Antics dot
11:02	com

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