1. All the molecules in sample of gas moves with different velocities. Therefore, we average out their velocities to go by our calculation of temperature.

2. The sole reason for averaging is to find that one value of velocity that we can assign to all the molecules and find the temperature of gas as per the definition which is – the average kinetic energy of molecules in a gas is directly proportional to temperature of the gas.

Where K. E=kinetic energy of gas

k_B = Boltzmann constant

T = temperature of gas

3. So yes, temperature of all molecules in a sample of a gas is the same.