Question

The following table shows the probability of rolling the numbers 1 through 6 on a fair die.
X-1,2,3,4,5,6
P(X)-1/6,1/6,1/6,1/6,1/6,1/6
What is the standard deviation of the random variable X, "the number that comes up on the die?"
A.14.028
B.2.917
C.3.5
D.3.745
E.1.708

Answer 1

I think it is E. but im not sure,. im kinda confused.

Answer 2

Did you find the mean already?

Answer 3

Nope E was just my guess. i have no iea how to do this.. lol

Answer 4

Haha okay. Here's your process.
1) Find the mean of X. Since you have 6 equally likely possibilities, just add up the 6 possible outcomes and divide by the number of outcomes.

Answer 5

Following so far? Tell me what mean value you get for X.

Answer 6

negative.. how do i set up these possibilities..
i dont understand what i add.

Answer 7

What are the possible outcomes of a single dice roll?

Answer 8

is it like 1/6*(1)

Answer 9

1/6*(2)

Answer 10

then find the mean of the answers

Answer 11

The possible outcomes are 1,2,3,4,5,and 6.
Sum those, divide by 6. That will tell you the AVERAGE value of a single roll.

Answer 12

3.5

Answer 13

ohhh,,, so thats it!

Answer 14

Right. Doesn't that make sense that 3.5 would be the average value of a single roll?

Answer 15

I know the mean now. I don't know the standard deviation yet. But it's not too hard to figure it out, now that I know the mean.

Answer 16

Indeed... I was thinking to hard about it,.

Answer 17

The answer isn't 3.5, by the way. 3.5 is the mean. They asked for the standard deviation. So we're almost there.

Answer 18

yeah i figured that.. lol its never just that easy..
is finding the standard deviation as easy.

Answer 19

Not QUITE as easy. But it's not too bad.
4 basic steps.
We have 6 possibilities. For each one, find out (x-3.5)^2 (So for example, 1 is one possibility, so I would do (1-3.5^2) = (-2.5)^2 = 6.25)
add all of those things up.
Divide that by N, the number of possibilities.
Square root that to get standard deviation.

Answer 20

alright,.. that works.

Answer 21

You understand each step that I'm asking you to do?

Answer 22

yea im pretty sure i got it.

Answer 23

Great =D As you do it, feel free to ask me for clarification.

Answer 24

alright so the second one would look like (2-3.5)=(-1.5)^2=2.5

Answer 25

Almost right. One tiny mistake. (-1.5)^2 = 2.25

Answer 26

ahh yeah that what i meant ;P the third one would =0.25

Answer 27

Right =)

Answer 28

so would the 4th one. =0.25

Answer 29

5th =2.25
6th=6.25

Answer 30

yup

Answer 31

and then add them all up an divide by 6?

Answer 32

Yes =)

Answer 33

=2.91

Answer 34

outstanding!

Answer 35

One more step!

Answer 36

awww man

Answer 37

(square root)

Answer 38

1.705....

Answer 39

So yeah. To recap, I know that whole process seemed long and complicated, but it's not too bad.
Step 1: Find the mean
Step 2: For each possibility, find the difference from the mean and square that.
Step 3: Add up all of the results and divide by the number of possibilities.
Step 4: Square root that to get SD.

Answer 40

Yes =)

Answer 41

MY GUESS WOULD HAVE BEEN RIGHT!

Answer 42

Yaaaaay! =D You're so smart.

Answer 43

I know it! :) i am a good guesser! Thank you for teaching me the steps tho i can only get so far with guessing :P

Answer 44

My pleasure!