Why dividing by the square of 12 when calculating the standard deviation of a uniform distribution?

Question

My teacher does not know the answer on this one, so maybe someone can help me out with this.

In case of uniformal distribution, the probability distribution for a uniform random variable can be calculated with some formulas. The standard deviation is calculated with the formula

St. dev. = d - c / square 12

d=the highest value
c=the lowest value.

I understand that d-c is the lenght of the posibilities for the variable. But why should we divide by square 12 to know the standard deviation. Where does this come from?

Formula as on page 263 of McClave, Benson, Sincich; Statistics for Business and Economics, 9th edition.

Instead of Square 12, I mean Square Root 12!!!

Answer 1

the variance is (a+b)^2/ 12, so the SD. is the sqrt of variance...

the denominator is root 12

Answer 2

variance = integral(x from c to d) (x-m)²f(x)dx

where m is the mean = (c+d)/2 and f(x) = 1/(d-c) is the probability density function. So

variance = integral(x from c to d) (x-m)²/(d-c) dx

The indefinite integral is 1/3(d-c) * (x-m)³, plug in x=d and x=c and subtract the two. We get

variance = 1/3(d-c) * (d-m)³ - 1/3(d-c) * (c-m)³
= 1/3r * [(r/2)³ - (-r/2)³] where r = d-c
= 1/3r * r³/4
= r²/12.

Answer 3

you may get it by employing estimating the section around the advise below the bell-formed curve. while the section is approximately sixty 8% of the full section below the curve, you may get the ordinary deviation.

Answer 4

TRy looking here;

http://en.wikipedia.org/wiki/Standard_deviation

I think your formula is wrong but the number you divide by is related to the nuber of samples you have.