akt715 wrote:
Bunuel wrote:
Official Solution:
Which of the following sets has the standard deviation greater than the standard deviation of set A={10, 12, 14, 16, 18, 20, 22, 24, 26, 28}
I. Set B, which consists of 10 first positive integers
II. Set C, which consists of 10 first positive odd numbers
III. Set D, which consists of 10 first prime numbers
A. set B only
B. set C only
C. set D only
D. sets C and D only
E. sets B, C and D
The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
Now, clearly set B={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less widespread than set A, so its standard deviation is less than the standard deviation of set A;
Set C={1, 3, 5, 7, 9, 11, 13, 15, 17, 19} is as widespread as set A, so its standard deviation equals to the standard deviation of set A (important property: if we add or subtract a constant to each term in a set the standard deviation will not change, since set A can be obtained by adding 9 to each term of set C, then the standard deviations of those sets are equal);
Set D={2, 3, 5, 7, 11, 13, 17, 19, 23, 29} is more widespread than set A, so its standard deviation is greater than the standard deviation of set A.
Answer: C
How can you say that set D is more widespread than set A , without calculating the mean.
A={10, 12, 14, 16, 18, 20, 22, 24, 26, 28}
D={2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
Set A is a set of 10 consecutive even integers, so the difference between consecutive terms is 2.
Set D is a set of 10 consecutive prime numbers, so the average difference between consecutive terms is greater than 2.
Therefore, set D is more widespread than set A.