(a)

Scenario: Suppose the value of Young's modulus () was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations:

Data
116.2 115.7 114.5 115.2 115.5

Problem: Calculate (in ).

Process: is equivalent to the mean of the observations.

Answer: .

(b)

Problem: Use the deviations calculated in part (a) to obtain the sample variance (in ). Use the deviations calculated in part (a) to obtain the sample standard deviation (in ).

Process: ...

Answer: and .

(c)

Problem: Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance (in ) of these transformed values.

Process: ...

Answer: .

Summary

If you change all of the values in a data set by the same value, the mean, variance, and standard deviation all remain the same.