Answer to Question #175234 in Statistics and Probability for anifowose

Question

answer for If the median mass of five chemical reagent bags in the store room is 6.5 kg and one further 7 kg bag of chemical reagent is added to the consignment, then: (a) the new median mass will be about 6.6 kg (b) the median will increase (c) it is impossible for the new median mass to be less than it was (d) it is impossible

Answer 1

Let $x_i=$ the mass of $i$th chemical reagent bag, $i=1,2,3,4,5.$

Then $x_3=$ 6.5 kg, $x_4\geq$ 6.5 kg.

If one further 7 kg bag of chemical reagent is added to the consignment, then

$$median=\dfrac{x_3+x_4}{2}\geq6.5\ kg$$

Therefore

(c) it is impossible for the new median mass to be less than it was.