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 rangeRangeThe range formula computes the difference between the range’s maximum and minimum values." To determine the range, the formula subtracts the minimum value from the maximum value. Range = maximum value – minimum value read more between 0 and 1. This normalization technique helps compare corresponding normalized values from two or more different data sets eliminating 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. Next, the minimum value deducts from the maximum value, and the previous result is divided by the latter.

Mathematically, the normalization equation represent as:

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Explanation of the Normalization Formula

Examples of Normalization Formula (with Excel Template)

To understand them better, let’s see some simple to advanced examples of normalization equations.

  • Firstly, identify the minimum and maximum values in the data set, denoted by x(minimum) and x(maximum). Next, calculate the range of the data set by deducting the minimum value from the maximum value. Range = x(maximum) – x(minimum) Next, determine how much more in value the variable is to normalize from the minimum value by deducting the minimum value from the variable, i.e., x – x(minimum). Finally, the formula for calculating the normalization of the variable x derives by dividing the expression in Step 3 by the expression in Step 2, as shown above.

Range = x(maximum) – x(minimum)

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

One can convert the value of 11.69 in the given data set on a 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 a recent science test. Present the test scores of all the students in the range of 0 to 1 with the help of normalization techniques. 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) = 0.48Score of student 3 = (56 – 37) / (95 – 37) = 0.33Score of student 4 = (87 – 37) / (95 – 37) = 0.86Score of student 5 = (91 – 37) / (95 – 37) = 0.93Score of student 6 = (37 – 37) / (95 – 37) = 0.00Score of student 7 = (49 – 37) / (95 – 37) = 0.21Score of student 8 = (77 – 37) / (95 – 37) = 0.69Score of student 9 = (62 – 37) / (95 – 37) = 0.43Score of student 10 = (59 – 37) / (95 – 37) = 0.38Score of student 11 = (95 – 37) / (95 – 37) = 1.00Score of student 12 = (63– 37) / (95 – 37) = 0.45Score of student 13 = (42 – 37) / (95 – 37) = 0.09Score of student 14 = (55 – 37) / (95 – 37) = 0.31Score of student 15 = (72 – 37) / (95 – 37) = 0.60Score of student 16 = (68 – 37) / (95 – 37) = 0.53Score of student 17 = (81 – 37) / (95 – 37) = 0.76Score of student 18 = (39 – 37) / (95 – 37) = 0.03Score of student 19 = (45 – 37) / (95 – 37) = 0.14Score 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.

Relevance and Use

The concept of normalization is very important because One may often use it in various fields, such as ratings. For example, one may use the normalization technique 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 distributionProbability DistributionProbability distribution could be defined as the table or equations showing respective probabilities of different possible outcomes of a defined event or scenario. In simple words, its calculation shows the possible outcome of an event with the relative possibility of occurrence or non-occurrence as required.read more 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 distributionNormal DistributionNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more. However, the technique can’t handle outliers very well, which is one of its primary limitations.

You can download this Normalization Formula Excel Template from here – Normalization Formula Excel Template

This article is a guide to Normalization Formula. Here, we discuss normalizing the given values, examples, and a downloadable Excel template. You can learn more about statistical modeling from the following articles: –

  • Formula of Poisson DistributionFormula of Normal DistributionStandard Normal Distribution FormulaWhat is the European Option?