Table $2$ gives height and weight data on $12$ people with their BMI classification, as

well as data on a $13-$th person with unknown BMI classification.

height weight

person m kg class

p$11\mathrm{.}8372$ normal

p$21\mathrm{.}8968$ normal

p$31\mathrm{.}71104$ serverely obese

p$41\mathrm{.}76100$ obese

p$51\mathrm{.}5659$ obese

p$61\mathrm{.}6695$ obese

p$71\mathrm{.}8981$ normal

p$81\mathrm{.}8677$ normal

p$91\mathrm{.}7695$ obese

p$101\mathrm{.}5350$ normal

p$111\mathrm{.}4645$ normal

p$121\mathrm{.}5359$ obese

p$131\mathrm{.}8080?$

Table $2$: Height and weight data with BMI classification.

$($a$)$ Use the Body Mass Index $($BMI$)$ formula $($given in the Appendix on p$.7$ to

calculate the BMI for each of the $13$ persons. Calculate the difference in BMI

between p$13$ and the $12$ known persons. Show the results in a table, and order

the BMI differences from low to high. Show the resulting ordering in your table.

Show all your calculations. $(7)$

$($b$)$ If we want to use kNN to classify the new instance, o$8,$ what would be a good

value for k$?$ Justify your answer. $(4)$

$($c$)$ Use kNN with k $=3,4,$ and $5$ to classify person p$13.$ Write your answer in the

form of a table showing the BMI, differences, and the order of people from this

$$distance$.$ Interpret your results in terms of the different values for k$.$