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Context. We investigate the behavior of the mass variance and the mass function of galaxy clusters in a mixed distribution model. Aims. Our aim is to find a relation between the mass variance at a 8 h −1 Mpc scale, σ 8 , and the parameter controlling the Gaussian deviation in the model, α 0 , and to constrain the non-Gaussianity using observational data at cluster scales. Methods. By assuming that the statistics of the density field is built as a weighted mixture of two components, a Gaussian + Lognormal distribution, we rewrite the mass variance expression and the mass function for galaxy clusters. Results. We find a relation between the mass variance at a 8 h −1 Mpc scale, σ 8 , and the scale parameter controlling the Gaussian deviation in the model, α 0 . This result, in conjunction with observational constraints on the mass variance and high-z galaxy clustering, suggests a scenario where structures develop earlier in comparison to strictly Gaussian models, even for α 0 0.003 Mpc. Our model also indicates that only well selected galaxy cluster samples at z 1 can discriminate between Gaussian and non-Gaussian (mixed) distribution models.