Step 1 :Chebyshev's theorem states that at least 1 - 1/k^2 of the data from a sample will fall within k standard deviations of the mean for all k > 1. In this case, k = \(\frac{6}{5}\).
Step 2 :We need to calculate 1 - 1/(\(\frac{6}{5}\))^2 to find the least possible fraction of the numbers in a data set lying within \(\frac{6}{5}\) standard deviations of the mean.
Step 3 :Final Answer: The least possible fraction of the numbers in a data set lying within \(\frac{6}{5}\) standard deviations of the mean is approximately 0.3056 or \(\boxed{\frac{61}{200}}\) when simplified as a fraction.