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This paper aims to characterize the ratio indicator proposed in reference . Ratio indicator enables the stochastic up and down method to have the ability to show users the precision of the estimation, so that waveform reconstruction with jittered data using the said method can be conducted in a reliable way. After studying in detail the stochastic stationary model, we initiate 15 random walks of decreasing threshold intervals and calculate the ninety-eighth percentiles of the corresponding stationary distributions. Analysis on the computing result enables us to find the characterization of ratio indicator. Our target is to advance the usage of ratio indicator. What is proved in the paper is that ratio indicator can be applied more rigorously to show the error bound of the estimation of the median.