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I tossed coin (fair) 10 times and collected data as follows:- H H T H H T H T H H what I did added "repeat" in observation if previous toss was same; like H (Repeat) H T H (Repeat) H T H T H (Repeat) H "(Repeat)" if last toss is same to previous results; could I establish any relationship between these two observations that next "Repeat" happens would be for T? Thanks in advance, Anoop, Sydney

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No, the point is that each new toss will be completely uncorellated to the previous ones. The exact situation you describe was analysed deeply here. The point is that you know the tosses tend to 50%-50%, but their difference does not converge at all.

The wikipedia image brings it to the point:

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The ratio of the tosses will converge but their difference won't, you cannot say anything about the next toss when knowing the previous ones.