We use a cluster sample selected independently of the intracluster medium content with reliable masses to measure the mean gas mass fraction and its scatter, the biases of the X-ray selection on gas mass fraction, and the covariance between the X-ray luminosity and gas mass. The sample is formed by 34 galaxy clusters in the nearby ($0.050<z<0.135$) Universe, mostly with $14<log M_{500}/M_odot lesssim 14.5$, and with masses calculated with the caustic technique. First, we found that integrated gas density profiles have similar shapes, extending earlier results based on subpopulations of clusters such as those that are relaxed or X-ray bright for their mass. Second, the X-ray unbiased selection of our sample allows us to unveil a variegate population of clusters; the gas mass fraction shows a scatter of $0.17pm0.04$ dex, possibly indicating a quite variable amount of feedback from cluster to cluster, which is larger than is found in previous samples targeting subpopulations of galaxy clusters, such as relaxed or X-ray bright clusters. The similarity of the gas density profiles induces an almost scatterless relation between X-ray luminosity, gas mass, and halo mass, and modulates selection effects in the halo gas mass fraction: gas-rich clusters are preferentially included in X-ray selected samples. The almost scatterless relation also fixes the relative scatters and slopes of the $L_X-M$ and $M_{gas}-M$ relations and makes core-excised X-ray luminosities and gas masses fully covariant. Therefore, cosmological or astrophysical studies involving X-ray or SZ selected samples need to account for both selection effects and covariance of the studied quantities with X-ray luminosity/SZ strength.
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