Let the seven numbers be

a,b,c,d,e,f,gBy question the sum of these seven numbers is \(84\)

Also by question, \(a+b+c+d = 32\) and

\(d+e+f+g = 80\)

If we sum the summation of 4 smallest numbers and 4 greatest numbers we get = 112

In other words \(a+b+c+2d+e+f+g = 112\). If we reduce the sum of all numbers i.e. 84 from this we get 28 which is the value for d

If we reduce d from the list of 4 greatest as well as 4 smallest number we get sum for 3 greatest numbers and 3 smallest numbers.

Therefore, new sums will be 52 and 4 their difference 48.

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes