The standard deviation of a sample is proportional to 1/√N where N is the sample size. In this case we are decreasing N by half, so we can write:
1/√(N/2) = √2 / √N
If we say that our standard deviation is proportional to 1/√N, the difference that occurred from decreasing the sample size by half resulted in an increase in the standard deviation by a factor of √2.
Therefore, the standard deviation is multiplied by √2.
