We (re)analyse the statistical properties of the following kinds of data series of solar activity phenomena: magnetic synoptic charts, hemispherical relative sunspot numbers, solar flare index, coronal index, solar radio flux, interplanetary magnetic field, and proton speed in the solar wind to find common mid-term periods during Solar Cycles 21-23. As a new approach we focus on the magnetic polarity relations to explore the connections between the several aspects of the solar activity from different points of view. At the investigation of the synoptic maps we define new quantities (e.g. positive-negative polarity asymmetry), and we carry out their time-series analysis. We used three different methods, namely the discrete Fourier-transform (DFT), the Lomb-Scargle periodogram (LSP), and the (Morlet) wavelet-transform (MWT). Naturally, we found the peaks arised from the well-known Schwabe and Hale cycles in every data sets. Besides, in the primarily studied 1.0-2.0-year interval we found common periodicities almost in the all data sets. (The only two exceptions are the coronal index and the solar radio flux data.) Based on the temporal distribution of the periods in the wavelet spectra we found connections between different data sets, which might suggest common origin.