You may use excel to answer questions. Copy relative results $($figures$,$ tables, plots$)$ generated while answering each question. Explain them if needed.

$1.$ Reduce the noise effect of the following data set with respect to the given binning techniques.

$2,2,3,3,13,15,16,16,19,20,20,21,22,22,25,25,25,25,30,33,33,33,35,35,35,35,35,35,36,40,45,46,52,70,71,77,78,80,81,81,81$

a$.$ Use the equal depth of $3$ and apply the $$mean$($you should complete this section by the Excel$)$

b$.$ Use the equal depth of $3$ and apply the $$boundaries$($you should complete this section by the Excel$)$

c$.$ Use the equal width method with the total of $6$ bins and apply $$boundaries$($ you should complete this section by the Excel$)$

$(9$marks$)$

$2.$ Use the methods below to normalize the following group of data:

$100,150,200,300,400,600,1000,1500,2000$

$($a$)$ min$-$max normalization by setting min $=0$ and max $=1(1$ marks$)$

$($b$)$ z$-$score normalization $(1$ marks$)$

$3.$ List the major steps considering in data preprocessing to prepare data for data mining analysis $(2$ marks$)$

$4.$ What is the range of Pearson test? Explain it$.(2$ marks$)$

$5.$ Assume that you measured the correlation between Age and income of MSUM staffs. Pearson test gave you a value of $0\mathrm{.}65.$ What do you understand from this value? $(2$ marks$)$

$6.$ How can we use correlation analysis $($Pearson text$)$ to reduce the number of decision variables? $($input variables$).(3$marks$)$