Formula of Normalization (Table of Contents)
What is Normalization Formula?
In statistics, the term “normalization” refers to the scaling down of the data set such that the normalized data falls in the range between 0 and 1. Such normalization techniques help in comparing corresponding normalized values from two or more different data sets in a way that it eliminates the effects of the variation in the scale of the data sets i.e. a data set with large values can be easily compared with a data set of smaller values.
The equation for normalization is derived by initially deducting the minimum value from the variable to be normalized, then the minimum value is deducted from the maximum value and then the previous result is divided by the latter.
Mathematically, Normalization equation is represented as,
Explanation of the Normalization Formula
The equation of calculation of normalization can be derived by using the following simple four steps:
Step 1: Firstly, identify the minimum and maximum value in the data set and they are denoted by x _{minimum} and x _{maximum}.
Step 2: Next, calculate the range of the data set by deducting the minimum value from the maximum value.
Range = x _{maximum} – x _{minimum}
Step 3: Next, determine how much more in value is the variable to normalized from the minimum value by deducting the minimum value from the variable i.e. x – x _{minimum}.
Step 4: Finally, the formula for the calculation of normalization of the variable x is derived by dividing the expression in step 3 by the expression in step 2 as shown above.
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Examples of Normalization Formula (with Excel Template)
Let’s see some simple to advanced examples of normalization equation to understand it better.
Normalization Formula – Example #1
Determine the normalized value of 11.69, i.e. on a scale of (0,1), if the data has the lowest and highest value of 3.65 and 22.78 respectively.
From the above, we have gathered the following information.
Therefore the calculation of the normalization value of 11.69 is as follows,
 x (normalized)= (11.69 – 3.65) / (22.78 – 3.65)
Normalization value of 11.69 is –
 x (normalized) = 0.42
The value of 11.69 in the given data set can be converted on the scale of (0,1) as 0.42.
Normalization Formula – Example #2
Let us take another example of a data set that represents the test marks scored by 20 students during the recent science test. Present the test scores of all the students in the range of 0 to 1with the help of normalization technique. The test scores (out of 100) are as follows:
As per given test score,
The highest test mark is scored by student 11 i.e. x _{maximum} = 95, and
The lowest test mark is scored by student 6 i.e. x _{minimum} = 37
So the calculation of the normalized score of student 1 is as follows,
 Normalized Score of student 1 = (78 – 37) / (95 – 37)
Normalized Score of student 1
 Normalized Score of student 1 = 0.71
Similarly, we have done the calculation of normalization of score for all the 20 students as follows,
 Score of student 2 = (65– 37) / (95 – 37) = 0.48
 Score of student 3 = (56 – 37) / (95 – 37) = 0.33
 Score of student 4 = (87 – 37) / (95 – 37) = 0.86
 Score of student 5 = (91 – 37) / (95 – 37) = 0.93
 Score of student 6 = (37 – 37) / (95 – 37) = 0.00
 Score of student 7 = (49 – 37) / (95 – 37) = 0.21
 Score of student 8 = (77 – 37) / (95 – 37) = 0.69
 Score of student 9 = (62 – 37) / (95 – 37) = 0.43
 Score of student 10 = (59 – 37) / (95 – 37) = 0.38
 Score of student 11 = (95 – 37) / (95 – 37) = 1.00
 Score of student 12 = (63– 37) / (95 – 37) = 0.45
 Score of student 13 = (42 – 37) / (95 – 37) = 0.09
 Score of student 14 = (55 – 37) / (95 – 37) = 0.31
 Score of student 15 = (72 – 37) / (95 – 37) = 0.60
 Score of student 16 = (68 – 37) / (95 – 37) = 0.53
 Score of student 17 = (81 – 37) / (95 – 37) = 0.76
 Score of student 18 = (39 – 37) / (95 – 37) = 0.03
 Score of student 19 = (45 – 37) / (95 – 37) = 0.14
 Score of student 20 = (49 – 37) / (95 – 37) = 0.21
Now, let us draw the graph for the normalized score of the students.
Normalization Formula Calculator
You can use this normalization formula calculator.
X  
X_{minimum}  
X_{maximum}  
X_{normalized}  
X_{normalized} = 


Relevance and Use
The concept of normalization is very important because it is often used in various fields, such as ratings where the normalization technique is used to adjust the values measured on different scales to a notionally common scale (0 to 1). The concept of normalization can also be used for more sophisticated and complicated adjustments like bringing the entire set of a probability distribution of adjusted values into alignment or quantile normalization in which the quantiles of different measures are brought into alignment.
It also finds application in educational assessment (as shown above) to align the scores of the students to a normal distribution. However, the technique can’t handle outliers very well which one of its primary limitation.
You can download this Normalization Formula Excel Template from here – Normalization Formula Excel Template
Recommended Articles
This has been a guide to Normalization Formula. Here we discuss how to normalize the given values along with examples and downloadable excel template. You can learn more about statistical modeling from the following articles –
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