1
00:00:00,720 --> 00:00:05,735
Find the mean, median, and mode of the following sets of numbers,

2
00:00:05,735 --> 00:00:07,361
and they give us the numbers right over here.

3
00:00:07,361 --> 00:00:09,404
So if someone just says "the mean",

4
00:00:09,404 --> 00:00:13,723
they're really referring to what we typically, in everyday language, call "the average".

5
00:00:13,723 --> 00:00:15,395
Sometimes it's called "the arithmetic mean"

6
00:00:15,395 --> 00:00:18,042
because you'll learn that there are actually other ways of calculating a mean.

7
00:00:18,042 --> 00:00:20,364
But it's really, you just sum up all of the numbers

8
00:00:20,364 --> 00:00:22,129
and you divide by the numbers there are.

9
00:00:22,129 --> 00:00:24,776
And so it's one way of measuring the central tendency

10
00:00:24,776 --> 00:00:27,051
or, you know, the average, I guess we could say.

11
00:00:27,051 --> 00:00:28,398
So this is our mean.

12
00:00:28,398 --> 00:00:31,649
We want to average 23 plus 29,

13
00:00:31,649 --> 00:00:41,773
or we want to sum 23 plus 29 plus 20 plus 32 plus 23 plus 21 plus 33 plus 25

14
00:00:41,773 --> 00:00:44,698
and then divide that by the number of numbers.

15
00:00:44,698 --> 00:00:49,900
So if [counting] 1, 2, 3, 4, 5, 6, 7, 8 numbers.

16
00:00:49,900 --> 00:00:51,479
So you want to divide that by 8.

17
00:00:51,479 --> 00:00:53,568
So let's figure out what that actually is.

18
00:00:53,568 --> 00:00:55,472
Actually, I'll just get the calculator out for this part.

19
00:00:55,472 --> 00:00:59,373
I could do it by hand, but we'll save some time over here.

20
00:00:59,373 --> 00:01:20,364
So we have 23 plus 29 plus 20 plus 20 plus 32 plus 23 plus 21 plus 33 plus 25.

21
00:01:20,364 --> 00:01:23,476
So the sum of all the numbers is 206,

22
00:01:23,476 --> 00:01:25,798
and then we want to divide 206 by 8.

23
00:01:25,798 --> 00:01:34,067
So, if I say 206 divided by 8 gets us 25.75.

24
00:01:34,067 --> 00:01:38,151
So the mean is equal to 25.75.

25
00:01:38,151 --> 00:01:41,030
So this is one way to kind of measure the center, the central tendency.

26
00:01:41,030 --> 00:01:45,302
Another way is with the median. And this is to pick out the middle number.

27
00:01:45,302 --> 00:01:47,485
The median.

28
00:01:47,485 --> 00:01:51,479
And to figure out the median, what we want to do is order these numbers from least to greatest.

29
00:01:51,479 --> 00:01:56,123
So it looks like the smallest number here is 20. Twenty.

30
00:01:56,123 --> 00:01:59,978
Then the next one is 21. Twenty-one.

31
00:01:59,978 --> 00:02:02,533
Then we go... there's no 22 here.

32
00:02:02,533 --> 00:02:07,361
There's uh, let's see here, there's two 23s... 23 and a 23.

33
00:02:07,361 --> 00:02:10,473
So twenty-three and a twenty-three.

34
00:02:10,473 --> 00:02:13,817
And no 24s. There is a 25. Twenty-five.

35
00:02:13,817 --> 00:02:18,693
There's no [counting] 26, 27, 28, there is a 29. Twenty-nine.

36
00:02:18,693 --> 00:02:24,637
And then you have your 32. Thirty-two. And then you have your 33. Thirty-three.

37
00:02:24,637 --> 00:02:26,448
So what's the middle number now that we've ordered it?

38
00:02:26,448 --> 00:02:30,814
So we have [counting] 1, 2, 3, 4, 5, 6, 7, 8 numbers; we already knew that.

39
00:02:30,814 --> 00:02:32,811
And so there's actually going to be two middles.

40
00:02:32,811 --> 00:02:37,455
If you have two... if you have an even number, there's actually two numbers that kind of qualify for

41
00:02:37,455 --> 00:02:40,705
close to the middle, and to actually get the median we're going average them.

42
00:02:40,705 --> 00:02:43,120
So, 23 will be one of them.

43
00:02:43,120 --> 00:02:44,467
That by itself can't be the median,

44
00:02:44,467 --> 00:02:47,133
because there's three less than it, and there's four greater than it.

45
00:02:47,133 --> 00:02:52,455
And 25 by itself can't be the median because there's three larger than it and four less than it.

46
00:02:52,455 --> 00:02:57,795
So what we do is we take the mean of these two numbers and we pick that as the median.

47
00:02:57,795 --> 00:03:05,365
So if you take 23 plus 25 divided by 2, that's 48 over 2 which is equal to 24.

48
00:03:05,365 --> 00:03:09,312
So even though 24 isn't one of these numbers, the median is 24.

49
00:03:09,312 --> 00:03:10,984
So this is the middle number.

50
00:03:10,984 --> 00:03:14,978
So once again, this is one way of thinking about central tendency.

51
00:03:14,978 --> 00:03:17,718
If you wanted a number that could somehow represent the middle,

52
00:03:17,718 --> 00:03:19,715
and I'm going to be clear, there's no one way of doing it.

53
00:03:19,715 --> 00:03:24,777
This is one way of measuring the middle, the middle, let me put that in quotes...

54
00:03:24,777 --> 00:03:28,446
the middle, if you had to represent this data with one number.

55
00:03:28,446 --> 00:03:31,046
And this is another way of representing the middle.

56
00:03:31,046 --> 00:03:33,368
Then finally, we can think about the mode.

57
00:03:33,368 --> 00:03:37,316
And the mode is just the number that shows up the most in this data set.

58
00:03:37,324 --> 00:03:42,470
And all of these numbers show up once except we have the 23 that shows up twice.

59
00:03:42,470 --> 00:03:46,789
And so twenty... since, since because 23 shows up the most,

60
00:03:46,789 --> 00:03:49,111
It shows up twice, every other number only shows up once,

61
00:03:49,204 --> 99:59:59,999
23... 23 is our mode.