Set M contains a set of consecutive integers. What is the standard deviation of set M?
(1) Set M contains 17 numbers
(2) The median of set M is 23
April 9th GMAT Question of the Day Solution:
Consecutive sets have special properties.
1. Median = Mean = (Max + Min)/2
2. Any consecutive set with the same number of numbers has the same standard deviation. For instance: The set 1, 2, 3 has the same standard deviation as 51, 52, 53 as will any set of 3 consecutive integers. So if you know the number of numbers you can figure out the standard deviation.
Statement (1) gives us the number of numbers in the set. Sufficient.
Statement (2) only gives us the median. The set could could be 22, 23, 24 or 21, 22, 23, 24, 25. These two sets have different standard deviations. Insufficient.