Data Sufficiency

Q: There is a set of consecutive even integers. What is the standard deviation of the set?
(1) There are 39 elements in the set.
(2) the mean of the set is 382.

Answer is a. Can Someone explain

hi jinglander,

this is a nice example of a statistics number properties question. for standard deviation, the number of terms in the set plays an important role in your ability to determine a value. in this problem, it is probably easier to start with the second statement as it is clearly insufficient.

(2) if the average of a set of consecutive even numbers is 382, it tells you that the set is evenly dispersed around 382 but you have no idea how many terms are in the set. For instance, the set could be {380, 382, 384} which would have a very small standard deviation, or the set could consist of 1001 consecutive even numbers with 382 as the middle term. Such a set would have a huge standard deviation as many terms would be very far from the mean. Not sufficient. Could be A,C,E.

(1) If you know that there are 39 terms in the set, this might appear at first glance to be insufficient. However, because the set consists of consecutive even numbers you can calculate the distances of each term from the mean (regardless of what that mean might be), which as you probably know is the key to determining standard deviation. Because there are an odd number of terms and you are dealing with an evenly spaced set, you know that the middle term is also the average (in all evenly spaced sets the mean = median). So you know that the middle term would have a difference of 0 from the mean. The two terms beside that in either direction would each of a distance 2 from mean, the next two terms would each have a difference of 4 from the mean, the next two would have a difference of 6 from the mean, and so forth. With this understanding, it is clear that you can determine how far each term is from the mean. If you know how far each term is from the mean, you can calculate the standard deviation and statement 1 alone is sufficient. Answer is A.

Also note on this problem that good data sufficiency strategy is key. Clearly, the intent of the test makers on this problem is for the test-taker to pick C, thinking that you need to actually know the mean. After getting it down to A and C, use your understanding of how standard deviation is calculated to avoid the trap of picking C. Hope this helps!

Hi Chris,

Would it have mattered if the number of elements was 38 instead of 39?

hi kvcpk,

the number of terms would not have mattered except that the average in statement 2 would have to be an odd number (as you probably know in data sufficiency the two statements cannot contradict each other). if you have a set of consecutive even numbers then the average will be odd if there are an even number of terms. for instance in the set [2,4,6,8] the average would be 5. with statement 1 you could determine the standard deviation regardless of how many terms they give you - its just that statement 2's average has to reflect that accurately. hope that answers your question and if not let me know...

chris@veritasprep wrote:hi kvcpk,

the number of terms would not have mattered except that the average in statement 2 would have to be an odd number (as you probably know in data sufficiency the two statements cannot contradict each other). if you have a set of consecutive even numbers then the average will be odd if there are an even number of terms. for instance in the set [2,4,6,8] the average would be 5. with statement 1 you could determine the standard deviation regardless of how many terms they give you - its just that statement 2's average has to reflect that accurately. hope that answers your question and if not let me know...

Thanks for your response Chris. I see what you are saying.

Other doubt I had was, If there is no use of statement 1, is it not a flaw in problem making?

In this case, statement1 was never needed to answer the question.

chris@veritasprep wrote:hi jinglander,

this is a nice example of a statistics number properties question. for standard deviation, the number of terms in the set plays an important role in your ability to determine a value. in this problem, it is probably easier to start with the second statement as it is clearly insufficient.

(2) if the average of a set of consecutive even numbers is 382, it tells you that the set is evenly dispersed around 382 but you have no idea how many terms are in the set. For instance, the set could be {380, 382, 384} which would have a very small standard deviation, or the set could consist of 1001 consecutive even numbers with 382 as the middle term. Such a set would have a huge standard deviation as many terms would be very far from the mean. Not sufficient. Could be A,C,E.

(1) If you know that there are 39 terms in the set, this might appear at first glance to be insufficient. However, because the set consists of consecutive even numbers you can calculate the distances of each term from the mean (regardless of what that mean might be), which as you probably know is the key to determining standard deviation. Because there are an odd number of terms and you are dealing with an evenly spaced set, you know that the middle term is also the average (in all evenly spaced sets the mean = median). So you know that the middle term would have a difference of 0 from the mean. The two terms beside that in either direction would each of a distance 2 from mean, the next two terms would each have a difference of 4 from the mean, the next two would have a difference of 6 from the mean, and so forth. With this understanding, it is clear that you can determine how far each term is from the mean. If you know how far each term is from the mean, you can calculate the standard deviation and statement 1 alone is sufficient. Answer is A.

Also note on this problem that good data sufficiency strategy is key. Clearly, the intent of the test makers on this problem is for the test-taker to pick C, thinking that you need to actually know the mean. After getting it down to A and C, use your understanding of how standard deviation is calculated to avoid the trap of picking C. Hope this helps!

What if the number of the element is even number does statement A still suff

Asma77 wrote:What if the number of the element is even number does statement A still suff

Yes, as long as you know what that even number is. For instance, if S1 said "There are 6 terms in the set", this would be enough (at least so long as we still know that the terms are consecutive even integers).

If S1 said "the number of terms in the set is even", however, we'd be out of luck - we could have 2 terms or 2,000,000 terms, each of which would have its own distinct standard deviation.