A secondary standard mass is periodically measured and compared to the standard for one kilogram (or 1000 grams). Listed below is a sample of measured masses (in micrograms) that the secondary standard is below the true mass of 1000 grams. One of the sample values is missing and is not shown below. The data are from the National Institutes of Standards and Technology, and the mean of the sample is 657.054 micrograms.

a. Find the missing value.

b. We need to create a list of n values that have a specific known mean. We are free to select any values we desire for some of the n values. How many of the n values can be freely assigned before the remaining values are determined? (The result is referred to as the number of degrees of freedom.)

675.04 665.10 631.27 671.35