Ans: (a) range $=73\text{ thousand dollars}$, inter-quartile range $=21\text{ thousand dollars}$ (b) mean $=54\text{ thousand dollars}$, median $=55\text{ thousand dollars}$
- The range
$\begin{array}{cl}
= & 91 – 18 \\
= & 73 \text{ thousand dollars}
\end{array}$The inter-quartile range
$\begin{array}{cl}
= & 63 – 42 \\
= & 21 \text{ thousand dollars}
\end{array}$ - The new mean
$\begin{array}{cl}
= & \dfrac{53\times 33 – 32 – 34 – 58 – 59}{29} \\
= & 54 \text{ thousand dollars}
\end{array}$Note that the old median is $55\text{ thousand dollars}$. Note also that among the four donated paintings, two paintings’ price are below the median and the other two are above the median. Hence, the median remains unchanged. i.e. the new median $= 55 \text{ thousand dollars}$
