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# how to find variance? Watch

1. how to find the variance from these numbers: (it's poisson distribution)
20 24 24 22 23
21 20 22 23 22
21 21 22 21 23
22 20 22 20 24

I know a long way of doing it:

mean = 21.85

minus the mean from each number then square it
then divide it by 20

I got 0.07 as the answer.

Is there a quicker way?
2. (Original post by 0utdoorz)
how to find the variance from these numbers: (it's poisson distribution)
20 24 24 22 23
21 20 22 23 22
21 21 22 21 23
22 20 22 20 24

I know a long way of doing it:

mean = 21.85

minus the mean from each number then square it
then divide it by 20

I got 0.07 as the answer.

Is there a quicker way?
You could knock 20 off each number to start with. It won't effect the variance, and the calculation becomes doable in your head - almost.

PS: I'd use E(X^2) - (E(X))^2 which avoids subtracting the mean from each numbers.
3. (Original post by ghostwalker)
You could knock 20 off each number to start with. It won't effect the variance, and the calculation becomes doable in your head - almost.

PS: I'd use E(X^2) - (E(X))^2 which avoids subtracting the mean from each numbers.
I tried that but for E(X^2) I got 103 (after dividing all the numbers by 20)

and the mean was 1.85

103 - 1.85^2 = 99.5775

is that right?
4. (Original post by 0utdoorz)
I tried that but for E(X^2) I got 103 (after dividing all the numbers by 20)
You get 103, as the sum of the squares after subtracting 20 from each number, but you still need to divide by 20.

So 103/20

and the mean was 1.85

103 - 1.85^2 = 99.5775

is that right?
Should be

103/20 - 1.85^2
5. (Original post by ghostwalker)
You get 103, as the sum of the squares after subtracting 20 from each number, but you still need to divide by 20.

So 103/20

Should be

103/20 - 1.85^2
would I keep the mean as the one after I divided each number by 20? or the original mean?
6. (Original post by 0utdoorz)
would I keep the mean as the one after I divided each number by 20? or the original mean?
Huh!

For the purposes of calculating the variance use the figures I put in my last post.

If you need the actual mean of the data, then it's clearly the original mean 21.85

What we're doing by subtracting 20 from each of the data items is, in effect, coding the data, with the formula Y= X-20

The variance of Y will equal the variance of X.
But the mean of Y will be the mean of X minus 20.

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Updated: April 15, 2013
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