SS Question $3$: K$-$Nearest Neighbours $[22]$ We have the height $($in cm$)$ and weight $($in kg$)$ dala of customers how have previously bought shirts at our store, showing the size of the shirts they bought, shown in Table $3.$ customer height weight shirt size $15858$ AT $15859$ M $15863$ M $16059)1116060$ M $16360$ M $16361$ M $16064$ L CO $16364$ Cle $16561$ L CH $16562$ L CH $16566$ L Cus $16862$ L C$416863$ L C $16866$ L CS $17063$ L Cut $17064$ L CLB $170681$ Table $3$: Shirt size data John comes into our store to buy a shirt. He is $1\mathrm{.}64$m tall, and weighs $62$kg$.($a$)$ Draw a diagram to show the relative position of all $18$ instances, as well as John's data. Label the diagram completely and correctly. $(5)($b$)$ Write down the formula to calculate the Manhattan distance between points M and Pin$($x$,$y$)-$space. Use this formula to calculate the distance between John and the first $12$ instances from Table $3.$ Rank the customers by their distances from John, trom closest to furthest. Show your workings. $(7)($c$)$ Show how $5-$NW $($k$-$nearest neighbours with $=5)$ will classity John's shirt size. Use the values in your calculations from the previous question. Show all your steps. $(3)($d$)$ Why is it important to standardise the data set when a classification algorithm such as k$-$NN is used? Use the data in Table $3$ as a reference to explain your answer. $(4)($e$)$ What does it mean when we say the k$-$NN algorithm is non$-$parametric? $(3)$