1
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Now that we know the mean and we also know what the range is.
2
00:00:06,940 --> 00:00:09,360
What we want to do is try to determine the standard deviation.
3
00:00:09,760 --> 00:00:14,170
Standard deviation is a measure of how spread out the numbers or the observations are
4
00:00:15,750 --> 00:00:16,920
in order to do s,.
5
00:00:16,930 --> 00:00:18,570
We need to find out what the variances is.
6
00:00:19,140 --> 00:00:20,070
For variance,
7
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we're going to use the following formula.
8
00:00:38,600 --> 00:00:41,980
We're gonna take our observations individually,
9
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subtract the mean from them,
10
00:00:46,640 --> 00:00:48,220
and we are going to square them.
11
00:00:48,500 --> 00:00:53,460
We will take those amounts and divide them by end
12
00:00:53,460 --> 00:00:54,100
minus one.
13
00:00:54,840 --> 00:00:56,370
14
00:00:57,840 --> 00:01:00,060
We have our observations,
15
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our average or mean.
16
00:01:08,840 --> 00:01:13,290
This would be our
17
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distance
18
00:01:18,540 --> 00:01:19,590
and our variance,
19
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which is the squared.
20
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amount 160
21
00:01:29,140 --> 00:01:29,950
170
22
00:01:34,940 --> 00:01:35,480
Listing all of our observations are mean will
23
00:01:35,490 --> 00:01:40,280
Listing all of our observations are mean will
24
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always be the same.
25
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We have a negative 18 centimeter distance,
26
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a negative 8, 7, 7,
27
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and 12.
28
00:01:58,540 --> 00:02:01,570
When we square each of these
29
00:02:05,540 --> 00:02:09,660
so 18 squared would be 324
30
00:02:12,140 --> 00:02:15,560
64 49
31
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49 and 144.
32
00:02:20,940 --> 00:02:22,950
This could be done with just a basic calculator.
33
00:02:24,830 --> 00:02:27,670
Now we get a total variance of 630.
34
00:02:27,670 --> 00:02:28,150
35
00:02:28,940 --> 00:02:30,500
Now that we have our total variance,
36
00:02:31,540 --> 00:02:35,860
What we need to do is divided by our total number of our observations less one,
37
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6 30 but by five minus one.
38
00:02:42,140 --> 00:02:46,660
So 630 divided by four equals
39
00:02:48,040 --> 00:02:53,010
157.50 So this would be what
40
00:02:53,020 --> 00:02:54,270
is called are variance.
41
00:02:57,440 --> 00:03:00,010
Now the standard deviation
42
00:03:02,340 --> 00:03:06,360
is going to be our variance.
43
00:03:11,940 --> 00:03:15,110
Standard deviation will be our variance
44
00:03:16,640 --> 00:03:17,360
square root.
45
00:03:19,140 --> 00:03:23,600
Here we can
46
00:03:23,890 --> 00:03:28,650
enter that in 157.50
47
00:03:28,660 --> 00:03:30,470
48
00:03:36,900 --> 00:03:41,740
and we get a standard deviation of
49
00:03:41,740 --> 00:03:44,850
12.55 centimeters.
50
00:03:47,940 --> 00:03:50,050
In looking at this,
51
00:03:51,440 --> 00:03:54,690
we can refer our standard deviation to any chart.
52
00:03:54,700 --> 00:03:54,860
53
00:03:54,860 --> 00:03:56,000
These air pretty standard numbers.
54
00:03:56,000 --> 00:03:57,260
This will be in your formula guide.
55
00:03:59,240 --> 00:04:03,850
You can see here that your average is typically fall along a bell curve.
56
00:04:04,540 --> 00:04:08,560
So in this case are mean would be 178 centimeters
57
00:04:10,440 --> 00:04:15,230
and one standard deviation in either direction would
58
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be plus 12.55
59
00:04:20,640 --> 00:04:22,770
and negative 12.55
60
00:04:25,340 --> 00:04:25,940
Now,
61
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from these points,
62
00:04:27,190 --> 00:04:31,180
68% of all observations and this is a standard number.
63
00:04:31,180 --> 00:04:31,890
When it comes to standard,
64
00:04:31,890 --> 00:04:36,740
deviations will fall between negative 1 to
65
00:04:36,750 --> 00:04:41,320
1 so plus minus your mean plus minus one standard deviation will have
66
00:04:41,320 --> 00:04:45,770
68% of all observations within two
67
00:04:47,040 --> 00:04:49,750
Within two will have 95% of all
68
00:04:51,640 --> 00:04:52,520
observations,
69
00:04:54,720 --> 00:04:59,410
and within three we'll have 99.7% of all
70
00:04:59,410 --> 00:05:00,190
observations.
71
00:05:00,740 --> 00:05:05,470
We can determined with standard deviations when
72
00:05:05,470 --> 00:05:10,420
determining men's heights in Canada that 99.7%
73
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of the population will fall between
74
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178 plus
75
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or minus
76
00:05:24,340 --> 00:05:26,560
12.55 times three.
77
00:05:28,140 --> 00:05:32,340
So that's approximately 37.65
78
00:05:32,560 --> 00:05:33,360
centimeters.
79
00:05:33,740 --> 00:05:37,770
So 178 so between about 140
80
00:05:38,240 --> 00:05:40,210
to 215 centimeters,
81
00:05:40,210 --> 00:05:42,950
you'll see 99.7% of the population fall within it.