How to compare standard deviations of different sample sizes

Question

• I am interested in estimating the value of an unknown, random variable, X.
• X changes over time. So, X = X(t) = X_t
• At specific time intervals, I estimate the value of X_t using 7 different methods.
• Some methods randomly fail in their estimation of X. i.e., they return a null value.
• Therefore, each estimate of X_t, returns a set of estimates (sample pool size = N_t) where N_t <= 7.
• I estimate X as the median of my sample of N data points.
• I want to compare the "spread" between the data points in each pool, across different pools. (In other words, how "close together" or "far apart" are the points in my sample pool of estimates at time t1, t2, ..., tn.)
• Let's call the sample standard deviation of the N points at time t, S(t) = S_t = stdDev(N_t)

Question

Would it be correct to compute a variable Y_t = S_t/N_t and compare Y_t across all estimates at times t1, t2, ... tn?

Or, alternatively, maybe the formula should be:

Y_t = S_t/(N_t-1)

In other words, conclude that higher values of Y_t represent a higher "spread" situation? And, therefore, less confidence in my estimate of X_t?