Lets us go to the classical context of the Maxwell Boltzmann distribution for ideal gases (that is a gaussian function with a maximum) to answer your question.
In this case the distribution of the speeds, will have a maximum a certain temperature, depending on other physical factors such as the mass.
Maxwell Boltzmann distributions have three kinds of speeds for their analysis in atomic and molecular gases:
The mean speed, this is the most used in experimental and statistical analysis
The most probable speed
The mean square speed
Please, a classical reference is:
Fundamentals of Statistical and Thermal Physics by Prof. Friederic Reif, McGraw-Hill, 1965.
A new textbook on the topic is:
Statistical Thermodynamics: An Engineering Approach by Prof. John W. Daily. Cambridge University Press, 2019.
The following attribution common license plot of the normalized probability density function depending at fixed room temperature for noble gases is taken from the wiki: