Question

I need someone with statistics to help me with Central Limit Theory! :)

Answer 1

I was given this Excel sheet and I need to answer:
"Follow the directions on the CLT discovery spreadsheet found in the Course Handouts folder. For your first post, complete the following sentence: "As the sample size increases, the mean tends to __________ and the standard deviation tends to ________.""

Answer 2

@thomaster

Answer 3

@wolfe8

Answer 4

when I delete K1 I go from 4.22 to 4.75 in Mean of the Sample Means
When I do it again, i get 4.785
4.775
4.35
4.38
4.4
4.33
4.42

Answer 5

The thing is, it changes everytime I close and open the program lol

Answer 6

@ganeshie8

Answer 7

@timo86m haha i'm tagging everyone please help D:

Answer 8

4.42 is first, 4.61 then 4.235

Answer 9

@Mertsj @precal

Answer 10

Sorry. Not a statistics person.

Answer 11

Do you know anyone who is?:P haha

Answer 12

@Luigi0210

Answer 13

@aaronq

Answer 14

@jim_thompson5910 :DDD please help

Answer 15

in each column A and B, there's the defined formula =INT(10*RAND())

so that means you'll have a random integer from 0 to 10

that's why it changes everytime you open the program

Answer 16

Okay :O So then when I press del in K1, how does the mean changing mean anything?

Answer 17

Because to answer the question of the mean increase or decrease, how could random numbers mean anything?

Answer 18

I'm not sure what you're asking

Answer 19

Okay wait I think I'm getting it lol.

Answer 20

and I think you meant to say "sample size increase"

Answer 21

because that's what it says above

Answer 22

There's multiple pages, Sized 2, 3, 5, 7, and 10 Samples

Answer 23

oh just noticed that

Answer 24

so as n increases, what's going on with the shape of the distribution?

Answer 25

Hmm, it's kinda strange honestly.. There doesn't seem to be any kind of universal answer

Answer 26

This is sized 2 samples

Answer 27

These are new numbers BTW so no longer refer to those posted before :P

Answer 28

Sized 3 samples

Answer 29

yeah it's randomly generated

Answer 30

sized 5

Answer 31

despite this randomness, the sample means will fit a pattern if you have a very large sample size

Answer 32

Right so when N gets large enough, it'll become a regular model

Answer 33

what's another name for "regular"

Answer 34

Bell shaped? Evenly distributed?

Answer 35

Sized 10 samples

Answer 36

what else

Answer 37

Gaussian? :P

Answer 38

standard? Idk there's a lot of names=[

Answer 39

I'm thinking of "normal" or "normal distribution"

but yes, there are a lot of ways to describe this distribution

Answer 40

as n increases, this distribution becomes more symmetrical about the mean and becomes more like a normal bell shaped curve

Answer 41

As the sample size increases, the mean tends to __________ and the standard deviation tends to ________.

Answer 42

So as the sample size increases, the mean tends to distribute normally and the standard deviation tends to decrease.

Answer 43

hmm well it depends on the context really

in this case, we have a uniform random variable from 0 to 10, so the mean is (0+10)/2 = 5

notice how as n increases, the mean of the sample means is approaching 5

if n was very very large, then the mean would effectively be 5

Answer 44

Well the mean of sized 10 samples is 4.368 and sized 7 is 4.45

Answer 45

4.45 is a bit off from 5, but that's because our sample size is relatively small

Answer 46

But how come it goes down when it hits 10?

Answer 47

http://puu.sh/7gPiR.png

Answer 48

well it's going to vary around 5 (both above and below it)

it will get closer and closer to 5 as n gets bigger

Answer 49

So: As the sample size increases, the mean tends to __________ and the standard deviation tends to ________.

Answer 50

the mean tends to approach 5 and the standard deviation decreases?

Answer 51

the standard deviation is a bit harder to explain

the numbers are drawn from a uniform random distribution (basically any number from 0 to 10 goes and each has an equal chance)

Answer 52

That makes sense but no matter how the numbers change, the standard deviation decreases as n increases

Answer 53

hmm one sec

Answer 54

Oh wait! I finally got one where sized 5 samples was smaller than sized 7

Answer 55

I think I found a formula

\[\Large s = \sqrt{\frac{1}{12}(b-a)^2}\]

but it doesn't seem to be working though

Answer 56

Haha, that's always great

Answer 57

=STDEV(I4:I103)

Answer 58

yeah that computes the standard deviation from i4 to i103

Answer 59

but I'm looking for a basic general formula that the standard deviation is approaching

Answer 60

>_< Haha

Answer 61

sadly I couldn't find anything, so I'm not sure what to do with that part

Answer 62

should I just say decreases and hope for the best?

Answer 63

it does look like it decreases, but I'm not sure if that's what they want