M05-07

Official Solution:


Which of the following datasets has the standard deviation greater than the standard deviation of set X = {-19, -17, -15, -13, -11} ?

A = {1, 3, 5, 7, 9}

B = {2, 4, 6, 8, 10}

C = {1, -1, -3, -5, -7}


A. Set A only
B. Set B only
C. Set C only
D. Sets A, B and C
E. None of the datasets


One important property of the standard deviation is that the standard deviation remains unchanged when we add or subtract a constant value to each term in the dataset. This is because the standard deviation is a measure of the variation of the data points from the mean, a measure of how widespread a given set is. When the standard deviation is low, the data points tend to be close to the mean, while a high standard deviation implies that the data is spread out over a broader range of values. Therefore, adding the same value to each term in a dataset does not change how widespread the dataset is, and thus does not change its standard deviation.

Take a close look at each dataset and note that they all consist of five terms with a common difference of 2. As a result, each dataset can be obtained by adding a constant value to each term of another set. For instance, by adding 20 to each term of dataset X, we can obtain dataset A; by adding 21 to each term of dataset X, we can obtain dataset B, and by adding 12 to each term of dataset X, we can obtain dataset C. As a consequence, the standard deviation of all these datasets is identical.


Answer: E