$($a$)$ The doctor of a school has measured the total number of steps that ten pupils in a $5$th grade class do every day. The resulting measurements$-$observations are:

$200,300,400,600,1000,100,250,500,700,950$

Assume the first five measurements$-$observations $($i$.$e$.,200,300,400,600,1000)$ are the training set that a data scientist will use when performing some data mining experiments. Assume that the the rest five measurements$-$observations $($i$.$e$.,100,250,500,700,950)$ are the testing set that the same data scientist will use.

The data scientist wants at first to perform standardization but he does not know how to do it and needs your help. Therefore you are required to normalize all above measurements$-$observations by performing z$-$score normalization.

$[8$ marks$]$