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Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?
I. r-2, s-2, t-2
II. 0, r-s, t-s
III. r-4, s+5, t-1
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
We may recall the rule that when we add or subtract the same constant to a set of numbers the standard deviation does not change. Let’s analyze each Roman Numeral:
I. r-2, s-2, t-2
Since 2 is subtracted from r, s, and t, the standard deviation is the same as that of r, s, and t.
II. 0, r-s, t-s
If we subtract s from r, s, and t, we have r - s, s - s = 0, and t - s, thus the standard deviation is the same as that of r, s, and t.
III. r-4, s+5, t-1
We see that since we subtract/add different numbers to r, s, and t, we do not have the same standard deviation as that of r, s, and t.
Answer: C