\displaystyle{f({1\over 2^n}\sum_{i=1}^{2^n}x_i)=f\Bigg ({1\over 2}\Bigg ({1\over 2^{n-1}}\sum_{i=1}^{2^{n-1}}x_i+{1\over 2^{n-1}}\sum_{i=2^{n-1}+1}^{2^n}x_i\Bigg)\Bigg )\le {1\over 2}\Bigg (f({1\over 2^{n-1}}\sum_{i=1}^{2^{n-1}}x_i)+f({1\over 2^{n-1}}\sum_{i=2^{n-1}+1}^{2^n}x_i)}\Bigg )