Ans: (a) Mean $=18$, median $=16$ (b) (i) $18$ (ii) No
- Mean $=18\mbox{ hours}$, median $=16\mbox{ hours}$.
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- $18\mbox{ hours}$
- Let $x\mbox{ hours}$ and $y\mbox{ hours}$ be the two other data added. Consider the mean of the four data added,
$\begin{array}{rcl}
\dfrac{x+y+19+20}{4} & = & 18 \\
x+y & = & 33
\end{array}$In order to have the same median found in (a), $x$ and $y$ must be both smaller than or equal to $16$. Therefore, the maximum value of the sum of $x$ and $y$ is $32$.
However, the sum of $x$ and $y$ must be $33$ in order to have the mean $18\mbox{ hours}$. Therefore, it is impossible that the new median is the same as the median found in (a).
