What are the real benefits of normalization (scaling values between 0 and 1) in statistics?

I am working on student data set in which I want to normalize the range of percentage to 0,1. But I am not clear with the actual benefits of normalizing a range.

• A lot of the answers are with respect to normalization (standardization), if this isn't what you are looking for could you please expand on how you are normalizing (scaling) your data. Are you just scaling the score range over the interval 0,1? – Jonathan Lisic May 14 '15 at 1:28

Normalizing the data is done so that all the input variables have the same treatment in the model and the coefficients of a model are not scaled with respect to the units of the inputs.

For instance, consider that you have a model that measures the aging of paintings based on room temperature, humidity and some other variables. If humidity is measured in litres per cubic metre and temperature in degrees Celsius, the coefficients in the model will be scaled accordingly and may have a high value for humidity and a low value for temperature (say). If you scale the variables, such as by using $(x- \mu)/\sigma$ or any other technique, variability in output due to unit change in input variables will be modeled more realistically.

You may wish to rescale the predicted output to interpret the results.

In regression, the $t$-values and $R^2$ values are not affected due to scaling or not scaling. However, interpreting the results becomes easier using scaling.

Some machine learning algorithms require the input data to be normalized in order to converge to a good result.

Let's take for example a data set where samples represent apartments and the features are the number of rooms and the surface area. The number of rooms would be in the range 1-10, and the surface area 200 - 2000 square feet.

I generated some bogus data to work with, both features are uniformly distributed and independent.

Before scaling, the data could look like this (note that the axes are proportional):

You can see that there is basically just one dimension to the data, because of the two orders of magnitude difference between the features.

After standard scaling, the data would look like this (note that the axes are proportional):

Now the data is nicely distributed and a logistic regression or SVM could do a much better job classifying the samples.