How is 10% transaction fee possible for a bitcoin transfer from coinbase to another exchange? I moved 0.01BTC from coinbase to another exchange and i got charged 0.001BTC for it. This is 10%!!. I understand concept of dynamic pricing depending on network crowding etc. However, how is 10% fee possible when many websites show that median transaction fee is still around 0.2-0.4%. Is it due a small size that i used (0.01BTC) in transfer. Is there anything i can do to avoid such high and conform with median?

Also, is there a way to avoid such high transfer fee on coinbase?
This is normal.  You can see on https://bitcoinfees.earn.com/ that BTC 0.001 is a pretty average fee right now.

You should not think of it as a percentage, since the fee for a transaction is not related to the amount of coins transacted.  Instead, it has to do with the size of the transaction in bytes, which is more a matter of its complexity (e.g. number of input transactions spent, number of addresses paid).  You'd have paid the same fee whether the amount you sent was BTC 0.0001 (in which case it would be a 1000% fee) or BTC 1 (an 0.1% fee).


  Also, is there a way to avoid such high transfer fee on coinbase?


No.  If you want the percent fee to look smaller, send larger amounts.  Or you could wait and see if fees go down in the future (they might or might not).