Variance and entropy are distinct metrics commonly used to measure the uncertainty of random variables. While variance
shows how a random variable spreads more than expected, entropy measures the uncertainty of an information approach; in
other words, it measures the average amount of information of a random variable. For both uniform and normal distributions,
variance is a measure of power entropy. Finding such a monotonic relationship between variance and entropy for a larger
class of these two distributions is very important and useful in signal processing, machine learning, information theory,
probability, and statistics. For example, it is used to reduce the errors of estimators and choose a strategy that gives, on
average, the greatest or nearly greatest reduction in the entropy of the distribution of the target location. The effectiveness
of this method is tested using simulations with mining assay models. In this article, the upper bound of the variance for
single-mode distributions, whose tails are heavier than the tails of exponential distributions, is created with the help of power
entropy.