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In this paper, the fluctuations of stock prices and trade volumes are investigated by the method of Zipf plot, where Zipf plot technique is frequently used in physics science. In the first part of the present paper, the data of stocks prices and trade volumes in Shanghai Stock Exchange and Shenzhen Stock Exchange is analyzed, the statistical properties of stocks prices and trade volumes are studied. We select the daily data for Chinese stock market during the years 2002-2006, by analyzing the data, we discuss the statistical properties of fat tails phenomena and the power law distributions for the daily stocks prices and trade volumes. In the second part, we consider the fat ails phenomena and the power law distributions of Shanghai Stock Exchange Index and Shenzhen Stock Exchange Index during the years 2001-2006 by Zipf plot method.