Question

Suppose a feature has the following values: x1=10, x2=12, x3=15,

x4=20.
1) Compute scaled x2 using normalization.
2) Compute scaled x2 using standardization.

Answer 1

Normalization involves rescaling data to a 0-1 range, while standardization rescales data to have a mean of 0 and standard deviation of 1. For x2=12, normalization would use the min and max of the data set, whereas standardization would use the data set mean and standard deviation.

Step-by-step explanation:

The student is asking how to compute the normalized and standardized values of a given feature, specifically for the value x2=12, given a set of values (x1=10, x2=12, x3=15, x4=20). Normalization typically involves rescaling the values of a feature so they range from 0 to 1. Standardization, on the other hand, involves rescaling data to have a mean of 0 and a standard deviation of 1 (also known as z-score normalization).

To normalize x2, we use the formula:

normalized_x2 = (x2 - min(x)) / (max(x) - min(x))

Where min(x) and max(x) are the minimum and maximum values in the set, respectively.

For standardization, the formula is:

standardized_x2 = (x2 - mean) / standard_deviation

Where mean is the average of the values x1 through x4, and standard_deviation is the sample standard deviation of these values.