00:01
Okay, we have 40 students with shoes.
00:05
Let's just, i guess, write them all on down.
00:10
Looks like some people have one, two, one shoe, two shoes, three shoes, four, five, six, no six, seven.
00:19
And those 12 people have five shoes, 12 people have four shoes, two, five and eight or the rest.
00:25
Okay, here we go.
00:27
So this is kind of what they give us.
00:29
They want us to find the sample mean.
00:31
Okay, we can do that right off the bat.
00:35
We're just going to add up every single value.
00:38
So 40 values we're adding in total, and we're going to divide it by 40.
00:43
So i guess mathematically add up everything divide by 40, okay, or which is n.
00:49
All right, so we've got two people with one shoe.
00:53
We've got five people with two shoes.
00:56
We've got three people with eight shoes, four people with 12 shoes.
01:01
And i'm just saying everything backwards.
01:03
12 people with five shoes and one person with seven shoes.
01:06
It doesn't matter.
01:07
We're just multiplying, adding everything together.
01:10
We'll divide that by 40.
01:12
So let's see we've got two here, 10, 24.
01:16
That's interesting.
01:18
More interesting.
01:19
They're all multiples of 12.
01:21
Let's see.
01:21
So we've got there's one, two multiples of 12, four multiples of 12, five right there.
01:28
One and two, three, four, seven, five.
01:30
12 multiples of 12.
01:32
So that right there is 144 from 12 times 12.
01:37
So in total on top, we've got 151 over 40 and it didn't turn out to be so nice.
01:43
Calculator says this mean is 3 .775.
01:47
Okay, so let's box that, save it for later.
01:51
Now next, find the sample standard deviation.
01:54
Okay, so basically we're going to compare every single value, every 40 students, sneaker compared to the mean, we're going to sum that total.
02:05
So we'll kind of write it like this.
02:08
We're going from i to n, which is 40.
02:12
We're going to subtract the mean.
02:13
We're going to square that.
02:15
And then we're going to divide the whole thing by the number of degrees of freedom.
02:19
Let's suggest n minus 1.
02:20
In this case, 39.
02:22
Ok, so that's going to be an enormous equation on top.
02:26
But we can simplify things, right? so let's say we're the first person, has one pair of shoe.
02:32
We'll subtract it from the mean, square that.
02:36
And then we're going to have to write it again.
02:38
May as well just write a two in front, right? this is going to happen twice.
02:42
We'll write a five in front for this next one.
02:45
Just kind of keep going here.
02:49
We got this situation happening eight times where you have three pairs of shoes, not too far off from the mean.
02:56
Let's see, we've got 12 times that four people.
03:00
Oh, hold that 12 people have four shoes.
03:03
They're very close to the mean also.
03:06
We can just keep going here.
03:11
And then somebody's got seven pairs of shoes.
03:15
I'll just leave the one because the eraser is too far.
03:20
Okay, there we go.
03:21
And we'll divide that whole entire thing by 39.
03:24
So you can plug everything into your calculator.
03:27
I'm just going to do this stepwise.
03:29
So now we minimize errors.
03:31
I'm doing 1 .1 minus 3 .7 .7 .5.
03:35
That gave me negative 2 .775.
03:37
I'm squaring that.
03:39
Okay, so i've got two times 7 .701.
03:42
I'm just going to leave it in the thousands because our mean was in the thousands.
03:47
You know, just keep things uniform.
03:50
Anyhow, we'll just keep going here.
03:53
2 minus 3 .775.
03:55
That gives me 1 .775, that's square that value.
04:00
I got 3 .151.
04:03
Okay.
04:05
Keep going.
04:08
.775 squared.
04:10
Recall, this is negative.
04:12
0 .775, but when you square it, it'll become positive.
04:14
So don't worry about putting the negative.
04:16
Just save a bit of time.
04:18
Since this is a long question, let's see.
04:22
Here we've got 4 minus 3 .775, just 0 .225.
04:28
Squared that.
04:29
That's 0 .051.
04:31
All right, lots of 6 is in the, i guess the 10 ,000th place is rounding up here.
04:40
The next one, 5 minus 3 .775, square that.
04:46
We got 1 .501.
04:49
Another six there.
04:50
And that's because, you know, a lot of this was, there's a, there's a lot of 40 in there.
04:56
12.
04:57
Anyhow, it doesn't matter.
04:58
It will have sixes.
05:01
7 minus 3 .775 squared.
05:05
All right.
05:06
And that one is going to be 10 .401, right? because we've got, you can see, he is very far off from the average.
05:15
And so there's this guy, right? or these two people.
05:19
Anyhow, so let's go ahead and not forget that we're going to divide this by 39 in the end.
05:25
Okay, let's do it all at once.
05:28
2 .7 .01 plus 5 times 3 .151 plus 8 times .601 358 plus 12 times .051 plus 12 times 1 .501 plus 10 .401.
05:55
All right.
05:57
I got 64 .99, we're divided by 39.
06:02
I got 1 .39.
06:05
I got 1 .5.
06:05
I got 1 .5 .5.
06:05
I got 1 .5 .5 .5.
06:06
I got 1 .5 .5 .5 .5.
06:07
666...