Suppose that for star *i*, there are *n*_{i} > 1 zero-point data. Here one
uses a standard expression to calculate

(A1) |

*f*_{j} is the *j*th value of [Fe/H] for star *i*, and the variance
*v*_{i} of the values of [Fe/H] is the square of the standard deviation per datum.

Since *v*_{i} is calculated from a finite data set, *v*_{i} itself has a finite
variance. If the *f*_{j} are normally distributed, the variance of *v*_{i} is
inversely proportional to (see Keeping
1962, Eq. [5.11.14], p. 110). Inverse-variance weighting will
then yield a weight which is proportional to , so the expression for
the mean variance becomes

(A2) |

with *N* being the total number of contributing stars. The
associated number of degrees of freedom is given by

(A3) |

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