Normalization Formula

In statistics, the term “normalization” refers to the scaling down of the data set such that the normalized data falls between 0 and 1. This normalization technique helps compare corresponding normalized values from two or more data sets.

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 with smaller values. The equation for normalization is derived by initially deducting the minimum value from the variable to be normalized. Next, the minimum value subtracts from the maximum value, and the previous result is divided by the latter.

• In statistics, "normalization" means the scaling down of the data set such that the normalized data falls between 0 and 1. 
• This technique compares the corresponding normalized values from two or more different data sets discarding the various effects in the data sets on the scale, i.e., a data set with large values can be easily compared with a smaller values dataset.
• Normalization is fundamental since one may often use it in various fields, such as ratings. It also finds application in educational assessment to align the student's score to a normal distribution. 

Data normalization formula is the method of scaling values to bring them to a common range. It is used to process any data set so that they become comparable to other data set and can be used by anyone who wants to understand and interpret it.

It is mainly used by professionals working with a huge data volume. The formula changes the data set, so their variation falls between 0 and 1. Thus, in the data normalization formula, the highest data point will have a value of one as the normalized value and the lowest data point will have zero as the normalized value. The decimal values of other data points will be between zero and one.

The process is also called feature selling and is mainly used in sets in which the two ends of the two extreme limits are known, and the data is more or less evenly distributed. It is frequently used by data analysts in modelling or forecasting.

Mathematically, the normalization equation represents as:

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

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)

The 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.

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 the 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 scores for all 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.

We can use this normalization formula calculator.

The concept of normalization is fundamental 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 formula in machine learning 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 is one of its primary limitations.

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

The formula has some important benefits as follows:

• Better accuracy – The normalization formula in machine learning helps in improving the accuracy levels of the algorithms used in machine learning and any other types of analysis involving huge data. It prevents any one variable from becoming dominant and gives equal importance to all variables.
• Better comparison- It facilitates data comparison across various units and scales. Since all data points are in a common range, they become comparable.
• Eliminates duplicacy – It help to reduce the duplication and redundancy and is very useful when the data set has multiple scales.
• Better visualization – The method makes the data simplee to interpret because it can be easily visualized and plotted in graphs. Creating charts and graphs become easy.
• Efficient data mining – The data mining algorithms become more efficient and accurate due to the standard normalization formula. The outliers are minimized, and data quality becomes better. Thus, useful results are derived.

Let us look at some of the limitations of the formula.

• Outlier sensitive – Outliers are data points that differ significantly from the other values. The formula is outlier sensitive, which can reduce its effectiveness.
• May not suit all data sets – The method may not suit all types of data, like the ones that are categorical or non-linear in nature.
• Bias – The method can bring in the problem of biasness during the choice of range. If the range is too wide or too narrow, then the result may be incorrect.
• Interpretation and communication are difficult – Sometime, the performance of the result of the standard normalization formula may not be straightforward, and it is further difficult to communicate it to the stakeholders.

Both the above techniques are used to change the data set to make it useful for statistical analysis. But there are some points of difference between them as follows:

• The former scales the different values of the data set to a particular range which is usually between zero and one and the latter changes the value of the variable where the mean is zero and the standard deviation is one.
• The former is more useful in case the variables rae very different from each other and we want to bring it to a fixed range whereas the latter is useful when we want to convert the data to a standard normal distribution.

Thus, both the methods have their own benefits and limitations but which method to choose depends on the requirement and the type of data.

This article is a guide to what is Normalization Formula. We explain how to calculate it with example, calculator, uses, benefits & limitations.. You can learn more about statistical modeling from the following articles: -

• Formula of Poisson Distribution
• Formula of Normal Distribution
• Standard Normal Distribution Formula
• What is the European Option?