$(20$ points$)$ Suppose that the data for analysis includes the attribute age. The age values for the data tuples are $($in increasing order$)$:

$14,16,17,17,19,20,20,21,22,22,25,25,25,25,30,33,33,35,35,35,35,36,40,$

$45,46,52,70.$

$($a$)$ Use smoothing by bin means to smooth the above data, using a bin depth of $3.$

Illustrate your steps.

$($b$)$ How might you determine outliers in the data?

$($c$)$ Use min$-$max normalization to transform the value $35$ for age onto the range $0$;$1.$