  Moments play a crucial role in investigating the characteristics of charged
particle multiplicities in high energy interactions. The success of any model
which describes the multiplicity data can be understood well by studying the
normalised and factorial moments of that distribution.~The Tsallis model is one
of the most successful models which describes the multiplicity spectra,
transverse momentum ($p_T$) spectra very precisely in high energy
interactions.~In our previous work we have used the Tsallis $q$-statistics to
describe the multiplicity distributions in leptonic and hadronic collisions at
various energies ranging from 14 GeV to 7 TeV.~In the present study we have
extended our analysis for calculating the moments using the Tsallis model for
$e^+e^-$ interactions at $\sqrt{s}$ = 91 to 206 GeV from the LEP data and for
$pp$ interactions at $\sqrt{s}$ = 0.9 to 7 TeV in various pseudo-rapidity
intervals from the CMS data at LHC. By using the Tsallis model we have also
calculated the average charged multiplicity and its dependence on energy.~It is
found that the moments and the mean multiplicities predicted by the Tsallis
model are in good agreement with the experimental values.~We have also
predicted the mean multiplicity at $\sqrt{s}$ = 500 GeV for $e^+e^-$ collisions
and at $\sqrt{s}$ = 14 TeV for $pp$ collisions in extreme pseudo-rapidity
interval, $|\eta|$ $<$ 2.4
