A digital image is a numerical representation of visual perception that can be manipulated according to specifications. In order to reduce the cost of storage and transmission, digital images are compressed. Depending upon the quality of reconstruction, compression methods are categorized as Lossy and Lossless compression. The lossless image compression techniques, where the exact recovery of data is possible, is the most challenging task considering the tradeoff between the compression ratio achieved and the quality of reconstruction. The inherent data redundancies like interpixel redundancy and coding redundancy in the image are exploited for this purpose. The interpixel redundancy is treated by decorrelation using Run-length Encoding, Predictive Coding, and other Transformation Coding techniques. While entropy-based coding can be achieved using Huffman codes, arithmetic codes, and the LZW algorithm, which eliminates the coding redundancy. During the implementation of these sequential coding algorithms, the direction used for data scanning plays an important role. A study of various image compression techniques using sequential coding schemes is presented in this paper. The experimentation on 100 gray-level images comprising 10 different classes is carried out to understand the effect of the direction of scanning of data on its compressibility. Depending upon this study the interrelation between the maximum length of the Run and compression achieved similarly the resultant number of Tuples and compression achieved is reported. Considering the fuzzy nature of these relations, fuzzy composition operations like max-min, min-max, and max-mean compositions are used for decision-making. In this way, a rational comment on which data scanning direction is suitable for a particular class of images is made in the conclusion.