Question $5$

Consider an attribute X of a data set that takes the values $($sorted in$\{1,2,3,...,9\}$

increasing order$).$ We apply two methods $($equal width and equal frequency$)$ to discretize the

attribute into $3$ bins. The bins obtained are shown below:

Equal Width: $1,2,3\{\},4,5,6,7,8\{\},\{9\}$

Equal Frequency: $1,2,3\{\},4,5,6\{\},\{7,89\}$

Explain what the effect will be of applying the following transformations on each

discretization method, i$.$e$.,$ whether the elements assigned to each bin can change if you

discretize the attribute after applying the transformations below. Note that denotes the$$

average value and denotes the standard deviation of attribute X$.$