Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
Re: For the set {2, 2, 3, 3, 4, 4, 5, 5, x}, which of the following values
[#permalink]
17 Sep 2021, 09:51
Carcass wrote:
For the set {2, 2, 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
-------------ASIDE---------------- For the purposes of the GRE, it's sufficient to think of Standard Deviation as the Average Distance from the Mean. Here's what I mean:
Consider these two sets: Set A {7,9,10,14} and set B {1,8,13,18} The mean of set A = 10 and the mean of set B = 10 How do the Standard Deviations compare? Well, since the numbers in set B deviate the more from the mean than do the numbers in set A, we can see that the standard deviation of set B must be greater than the standard deviation of set A.
Alternatively, let's examine the Average Distance from the Mean for each set.
Set A {7,9,10,14} Mean = 10 7 is a distance of 3 from the mean of 10 9 is a distance of 1 from the mean of 10 10 is a distance of 0 from the mean of 10 14 is a distance of 4 from the mean of 10 So, the average distance from the mean = (3+1+0+4)/4 = 2
B {1,8,13,18} Mean = 10 1 is a distance of 9 from the mean of 10 8 is a distance of 2 from the mean of 10 13 is a distance of 3 from the mean of 10 18 is a distance of 8 from the mean of 10 So, the average distance from the mean = (9+2+3+8)/4 = 5.5
IMPORTANT: I'm not saying that the Standard Deviation of set A equals 2, and I'm not saying that the Standard Deviation of set B equals 5.5 (They are reasonably close however).
What I am saying is that the average distance from the mean can help us see that the standard deviation of set B must be greater than the standard deviation of set A. More importantly, the average distance from the mean is a useful way to think of standard deviation. This model is a convenient way to handle most standard deviation questions on the GRE. -----ONTO THE QUESTION!!!---------------------------
Remove x from the original set. The set {2, 2, 3, 3, 4, 4, 5, 5} has a mean of 3.5
In order to affect the greatest increase in the standard deviation, x must be the furthest from the mean (3.5)
Check the answer choices ..... answer choice A is furthest from the mean.