Indirect measurement is a quantity calculated by formula. Generally, the relative error of such quantities is obtained first, and then the standard deviation is obtained by using the relationship between relative error and standard deviation and average value.

For example, in the experiment of measuring solid density by buoyancy method, the density p=(m/m-m 1)p0, in which the standard deviations of m, m 1 p0 can be found, and the relative error of p is required first.

1 logarithmic density formula, and then find the total differential.

lnp=lnm-ln(m-m 1)+lnp0

DP/p = DM/m-(DM-DM 1)/(m-m 1)+dp0/P0

2 merge the same variable to get

DP/p =[-m 1/m(m-m 1)]DM+[ 1/(m-m 1)]DM 1+( 1/P0)dp0

3 Replace the differential sign with the standard deviation sign, and add the squares of each term to get the relative error.

E=a/p (average) = = [m1/m (m-m1)] 2.dm2+[1/(m-m1)] 2.dm265438+.

Standard deviation a=p (mean) xE