Sizes of the sunspots vary in a wide range during the progression of a solar cycle. Long-term variation study of different sunspot sizes are key to better understand the underlying process of sunspot formation and their connection to the solar dynamo. Kodaikanal white-light digitized archive provides daily sunspot observations for a period of 90 years (1921-2011). Using different size criteria on the detected individual sunspots, we have generated yearly averaged sunspot area time series for the full Sun as well as for the individual hemispheres. In this paper, we have used the sunspot area values instead of sunspot numbers used in earlier studies. Analysis of these different time series show that different properties of the sunspot cycles depend on the sunspot sizes. The `odd-even rule, double peaks during the cycle maxima and the long-term periodicities in the area data are found to be present for specific sunspot sizes and are absent or not so prominent in other size ranges. Apart from that, we also find a range of periodicities in the asymmetry index which have a dependency on the sunspot sizes. These statistical differences in the different size ranges may indicate that a complex dynamo action is responsible for the generation and dynamics of sunspots with different sizes.
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