How to deal with a skewed data-set having all the samples almost similar? I have a very large skewed training set where every feature's data-points are very similar ?

For example, following is some part of the training data :

93.65034,94.50283,94.6677,94.20174,94.93986,95.21071,1
94.13783,94.61797,94.50526,95.66091,95.99478,95.12608,1
94.0238,93.95445,94.77115,94.65469,95.08566,94.97906,1
94.36343,94.32839,95.33167,95.24738,94.57213,95.05634,1
94.65813,94.65246,94.64984,95.29596,95.14167,95.39941,1
95.50876,94.45346,95.23837,95.26877,94.84924,94.8021,0
94.5774,93.92291,94.96261,95.40926,95.97659,95.17691,0
93.76617,94.27253,94.38002,94.28448,94.19957,94.98924,0


where the last column is the class-label - only 0 and 1.

This only a part of the dataset, but the actual dataset contains about 95% of samples with class-label being 1, and the rest with class-label being 0, despite the fact that more or less all the samples are very much similar.

Please suggest an appropriate classifier (using scikit-learn) as well.
This is the so-called "Class Imbalance Problem". Fortunately, there are a number of possible approaches. 

Probably easiest is going to be to use the class_weight option present in a number of scikit-learn's classifiers. For example, LogisticRegression.

You can either set this option to "balanced" (or "auto" if you're using an older version of sklearn), in which case it automatically adjusts weights inversely proportional to class frequency (i.e. it tries to compensate for the class imbalance); or you can manually set the weights for each class label using a dict, e.g. {0:1, 1: 20}.

For a worked example using an SVM, see here.

See here for more information: https://stats.stackexchange.com/questions/131255/class-imbalance-in-supervised-machine-learning