Confidence intervals for Totals

If you know Total and Number of Items, you know the Average (Average) = (Total) / (Number of Items)

If you know Average and Number of Items, you know the Total

(Number of Items) = (Average) x (Total)

If you have a confidence interval for a population Average and Number of Items, you have a confidence interval for the population Total

Example:

Suppose an organization owns 1000 computers. In a random sample of 25 of these, the average value, allowing for depreciation, is $2330 and the standard deviation is $200. The usual 95% interval -- $ 2330 ± 2x200/5
$ 2250 to $ 2410 A confidence interval for the total value of all 1000 computers is $ 2,250,000 to $ 2,410,000

Conversely, if

$2,250,000 to $ 2,410,000 be a 95% confidence interval for the total value of all 1000 computers, a (95%) confidence interval for the average value is $2,250 to $ 2,410