# Sample mean and sample variance

1. Feb 19, 2008

### Shackman

The problem statement, all variables and given/known data
The sample mean and sample variance of five data values are, respectively, 104 and 4. If three of the data values are 102 100 and 105, what are the other two values?

The attempt at a solution
My idea was to get two equations for the two unknowns, let's call them x and y. The equation from the sample mean was easy enough to find.

(102 + 100 + 105 + x + y) / 5 = 104
102 + 100 + 105 + x + y = 520
x + y = 213

The equation obtained from the sample variance is way more difficult because of the algebra. I start off ((102-104)^2 + (100-104)^2 + (105 - 100)^2 + (x-104)^2 + (y-104)^2)/4 = 4. As you can see this will get messy in a hurry, when you substitute for x or y using the sample mean equation it will be a fourth degree polynomial. Is there an easier way to do this?

Last edited: Feb 20, 2008
2. Feb 20, 2008

### EnumaElish

An alternative equation you can use is $\sum_i x_i^2/n-(\bar x)^2$ = 4.