-
Jinglander
- Senior | Next Rank: 100 Posts
- Posts: 58
- Joined: Thu Jul 22, 2010 5:40 pm
- Thanked: 1 times
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!
