# Mean, Deviation (DEV), and Average (DEV)? question

1. Aug 28, 2011

### lolzwhut?

For the following data set of eight values, give the MEAN, DEVIATION (DEV), and AVERAGE DEVIATION (AD). Show a sample calculation for each: 0.77, 0.92, 1.12, 1.00, 0.96, 0.88, 1.16, 1.02

2. Relevant equations
Well before we began, can anyone take the courtesy and see if I'm getting the correct answer?

MEAN: 0.97875
DEV: .0126 (maybe?)

3. The attempt at a solution

DEV:
(-167/800)^2+(-47/800)^2+(113/800)^2+(-3/160)^2+(-79/808)^2+(29/160)^2+(33/800)^2 = 0.111635/(8-1) = 0.0159 =sqrt(0.0159)=0.126

I'm confused now....I think I found the standard deviation. However, I'm unsure how to even calculate the average deviation cause I don't have enough values. what am i doing wrong? What should I do next?

2. Aug 29, 2011

### lanedance

mean looks good
$$\mu = \frac{1}{n}\sum_i x_i$$
terminology, generally I would consider:
standard deviation (square root of variance)
$$\sigma = \sqrt{\frac{1}{n}\sum_i (x_i-\mu)^2}$$
sample standard deviation (square root of sample variance)
$$s = \sqrt{\frac{1}{n-1}\sum_i (x_i-\mu)^2}$$

looks like you are calculating the sample deviation (based on the (8-1) term)

Last edited: Aug 29, 2011
3. Aug 29, 2011

### lanedance

Also though I cpiece together what you are attempting, writing it like this may confuse things for other people, in particular
which doesn't make any sense

it would be better to be break it up into

DEV^2 = (-167/800)^2+(-47/800)^2+(113/800)^2+(-3/160)^2+(-79/808)^2+(29/160)^2+(33/800)^2 = 0.111635/(8-1) = 0.0159

DEV=sqrt(0.0159)=0.126

sorry if it comes across as pedantic, but if its clear what you're attempting you'll generally get a better and quicker answer (probably in test as well)

Last edited: Aug 29, 2011