Let's do analysis of the question this question is checking three aspects of maths - Exponents, Statistics and PEMDAS Rules.
1) Exponents - if fraction is raised to the -ve power convert that fraction into reciprocal and then make exponent positive (BCZ exponents are always positive)
2) Statistics - Median def
3) PEMDAS - first off all raise the power or take root of the number then apply the -ve sign.
1) -(1/2)^(-1/3) = - {(2)^1/3}~ -1.25
2)-(1/4)^(-1/3)= -{(4)^1/3} ~-1.5
3)-(1/4)^(-1/2)= - {(4)^1/2}~-2
4)-(1/4)^(-2/3)= -{(4)^2/3} ~ -2.49
5) -(1/3)^(-1/2) =- {(3)^1/2} ~ -1.73
arrange the above terms in ascending way: -2.49 , -2 , -1.73, -1.58 , -1.25
the middle term is -1.73 hence the option is E .(IMO)
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