gettinit wrote:
J is a collection of four odd integers whose range is 4. The standard deviation of J must be one of how many numbers?
a 3
b 4
c 5
d 6
e 7
Please explain your thought process on this one. Thanks
This is a good question though I did not like the wording very much. Instead of 'SD of J must be one one how many numbers', 'How many distinct values can SD of J take' is better. Anyway,
First I thought J is a set of four odd integers with range 4 so I said J = {1, x, y, 5}
Now x and y can take 3 different values: 1, 3 or 5
Either both x and y are same. This can be done in 3 ways.
Or x and y are different. This can be done in 3C2 ways = 3 ways
Total x and y can take values in 3 + 3 = 6 ways
Let me enumerate them for clarification:
{1, 1, 1, 5}, {1, 3, 3, 5}, {1, 5, 5, 5}, {1, 1, 3, 5}, {1, 1, 5, 5}, {1, 3, 5, 5}
These are the 6 ways in which you can choose the numbers.
Important thing: SD of {1, 1, 1, 5} and {1, 5, 5, 5} is same. Why?
SD measures distance from mean. It has nothing to do with the actual value of mean and actual value of numbers.
In {1, 1, 1, 5}, mean is 2. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean.
In {1, 5, 5, 5}, mean is 4. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean.
Similarly, {1, 1, 3, 5} and {1, 3, 5, 5} will have the same SD.
Then, {1, 3, 3, 5} will have a distinct SD and {1, 1, 5, 5} will have a distinct SD.
In all, there are 4 different values that SD can take in such a case.
Note: It doesn't matter what the actual numbers are. SD of 1, 3, 5, 7 is the same as SD of 12, 14, 16, 18. For detailed explanation of SD and how to calculate it, check the theory or Stats.
_________________
Karishma
Veritas Prep GMAT Instructor
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