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The following sets each have a mean of 10 and the standard deviations are given as variables.
Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P
Set II = {10, 10, 10, 10, 10, 10}, standard deviation = Q
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = R
Rank these three standard deviations from least to greatest.
A. P, Q, R
B. P, R, Q
C. Q, P, R
D. Q, R, P
E. R, Q, P
Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P
Set II = {10, 10, 10, 10, 10, 10}, standard deviation = Q
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = R
Rank these three standard deviations from least to greatest.
A. P, Q, R
B. P, R, Q
C. Q, P, R
D. Q, R, P
E. R, Q, P
22 Feb 2022, 10:51
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Bunuel
The following sets each have a mean of 10 and the standard deviations are given as variables.
Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P
Set II = {10, 10, 10, 10, 10, 10}, standard deviation = Q
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = R
Rank these three standard deviations from least to greatest.
A. P, Q, R
B. P, R, Q
C. Q, P, R
D. Q, R, P
E. R, Q, P
Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P
Set II = {10, 10, 10, 10, 10, 10}, standard deviation = Q
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = R
Rank these three standard deviations from least to greatest.
A. P, Q, R
B. P, R, Q
C. Q, P, R
D. Q, R, P
E. R, Q, P
Since the numbers in set II are the same, the standard deviation of that set is 0.
In other words, Q = 0.
Since all standard deviations are greater than or equal to 0, we know that Q is the smallest standard deviation, which means the correct answer is either C or D.
For the remaining two sets, it's sufficient to think of Standard Deviation as the Average Distance from the Mean (see the video below for more on this)
For set I, we can see that:
7 is 3 away from the mean of 10.
8 is 2 away from the mean of 10.
9 is 1 away from the mean of 10.
11 is 1 away from the mean of 10.
12 is 2 away from the mean of 10.
13 is 3 away from the mean of 10.
For set III, we can see that:
6 is 4 away from the mean of 10.
6 is 4 away from the mean of 10.
6 is 4 away from the mean of 10.
14 is 4 away from the mean of 10.
14 is 4 away from the mean of 10.
14 is 4 away from the mean of 10.
At this point, we can see that the average distance from the mean for set I will be smaller than the average distance from the mean for set III.
This means, the standard deviation of set I (aka P) will be less than the standard deviation of set III (aka R)
So the ordering is as follows: Q < P < R
Answer: C
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