2. The table below shows the scores achieved by a group of students on an exam.ID 1 2 3 4 5 6 7 8 9 10SCORE 42475927844972437359ID 11121314151617181920SCORE 58825079897570596735Using this data, perform the following tasks on the SCORE feature:a. A range normalization that generates data in the range(0,1)b. A range normalization that generates data in the range(-1, 1)
Question
- The table below shows the scores achieved by a group of students on an exam.ID 1 2 3 4 5 6 7 8 9 10SCORE 42475927844972437359ID 11121314151617181920SCORE 58825079897570596735Using this data, perform the following tasks on the SCORE feature:a. A range normalization that generates data in the range(0,1)b. A range normalization that generates data in the range(-1, 1)
Solution
To perform the tasks, we first need to understand what range normalization is. Range normalization is a scaling technique where the values are shifted and rescaled so that they end up ranging between a specified minimum and maximum value.
a. Range normalization to generate data in the range (0,1):
The formula for range normalization is:
X' = (X - Xmin) / (Xmax - Xmin)
where X is the original value, X' is the normalized value, and Xmin and Xmax are the minimum and maximum values in the original data, respectively.
First, we need to find the minimum and maximum scores in the data. The minimum score is 27 and the maximum score is 98.
Let's take the first score (42) as an example. Plugging the values into the formula, we get:
X' = (42 - 27) / (98 - 27) = 0.20
We would then repeat this process for each score in the data set.
b. Range normalization to generate data in the range (-1,1):
The formula for this type of normalization is:
X' = 2 * ((X - Xmin) / (Xmax - Xmin)) - 1
Again, let's take the first score (42) as an example. Plugging the values into the formula, we get:
X' =
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