Question

Consider the data set {100, 200, 300, 400, 500}. Choose all that apply.
A. None of the data are within one standard deviation of the mean.

B. all of the data are within two standard deviations of the mean.

C. all the data are within one standard deviation of the mean.

D. The data are distributed symmetrically about the mean.

Answer 1

I know for sure D and c and definitely not A, but Im not sure about B... If its within 1 deviation, does that mean it would be within 2 deviations as well?

Answer 2

@paigeRG What did you get for the mean and standard deviation of this data set?

Answer 3

300 for the mean and 158 deviation

Answer 4

Okay, I agree with that.

Answer 5

300 +/- 158 --> Are all the data within this interval?

Answer 6

yes

Answer 7

How do you know this is true for sure:

C. all the data are within one standard deviation of the mean.

Answer 8

oh, wait by all did you mean ALL?it was just that each number was with in the same interval as eachother

Answer 9

*I thought it was

Answer 10

Are all the data points between 142 and 458?

I think I see some data points that are outside that interval.

Answer 11

no thay arent

Answer 12

100 and 500 are outside the limits of the mean +/- 1 s.d.

Answer 13

So, option C is out, I think.

Answer 14

so the data would be within 2 deviations right?

Answer 15

300+/- 316 ??

Answer 16

So then it would be D and B am I correct?

Answer 17

300+/- 316 would give an interval between -16 and 616. I would vote "yes" for B. all of the data are within two standard deviations of the mean.

Answer 18

Why do you think this is true: D. The data are distributed symmetrically about the mean.

I am just now thinking about that option but you may already know.

Answer 19

Because they are evenly disbursed about the mean on either side (higher or lower than 300) but then again, since 500 isn't equal to 100 and 400 isn't equal to 200 then... does that mean they ARENT symmetrical?

Answer 20

That's what I think.

　The shape of a distribution is described by the following characteristics.
Symmetry. When it is graphed, a symmetric distribution can be divided at the center so that each half is a mirror image of the other.

http://stattrek.com/statistics/charts/data-patterns.aspx

Answer 21

I think the data points are symmetric about the mean.

That would make this true: D. The data are distributed symmetrically about the mean.

Answer 22

I see I see...

Answer 23

thank you !

Answer 24

You are welcome.