If two of the ten numbers 1, 3, 5, 7, 9, 11, 13, 17, 19, and 21 are picked out, is the deviation of the remain numbers same to that of ten numbers?
1). The median of remain numbers is 10
2). The mean of remain numbers is same to that of 10 numbers.

Good question, +1 too. I picked E. I am not sure how to solve it. I just think that if you remove two numbers, the whole std must change.
Not sure, I would like to see the solution.

Can you prove this?

I think we have something like this:

\sigma_{old}=\sqrt{\frac{\sum}{10}}

\sigma_{new}=\sqrt{\frac{\sum-(1-x_{av})^2-(21-x_{av})^2}{8}}

and \sigma_{old}<>\sigma_{new}
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Very interesting question

Give me two numbers for which \sigma_{new}=\sigma_{old}. Otherwise, 1 is sufficient
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I really don't know how we can prove this for 2min.
eschn3am, what do you think?
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Mean:

Find the difference between each term and mean and square it:












Now sum up the squares and divide it by the number of terms:



Now find the square root of the new number:



Now we have our standard deviation of 6.51099. For us to be able to pull ANY two numbers out and maintain our standard deviation we need to have specific numbers available to us. The total divided by 10 is equal to 42.393. We need a total of 8 numbers that, when divided by 8, equal 43.393. SO...



and



The only way we could pull two numbers out of this and maintain our standard deviation is by pulling two numbers whose difference of squares sums up to 84.786.

I don't believe those two numbers exist in our list, so any numbers you pull out will change the standard deviation.


This is a strange problem because there aren't any numbers you can remove and still keep the same standard deviation. Does that make the answer D or E? You know none of the numbers will work even without looking at the statements...bizarre.


HOWEVER...if you run the same problem with 11 numbers and include 15 again you have a real problem. The standard deviation works out so that you can pull a couple numbers that have a difference of squares = to 80 and it will all work out. Then we can use the statements to see if those are the numbers being pulled. Where did this problem come from? I'm almost positive you wouldn't see something like this on the actual test.