What Is the Normalization Formula? (With Uses and How-To)

By Indeed Editorial Team

Published May 21, 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

In statistics, one of the most common tools professionals uses to analyze data is the normalization method. This is an important process that can help you compare data sets. If you work with data, understanding the normalization technique and how it differs from standardization techniques can help you calculate more accurately and know which to use in different situations. In this article, we discuss the normalization formula, explain its uses, explore how to use it, review reasons for using this technique, consider the normalization technique for custom ranges, evaluate similar analysis techniques in statistics, and compare normalization versus standardization.

What is the normalization formula?

The normalization formula is a statistical formula that you can use to scale down a data set for all its variations to fall below one and zero. It helps you represent data points as values between one and zero. The largest data has a normalized value of one, and the smallest data point has zero. The other data points within one and zero have decimal values in proportion to their locations within the data set range. This technique also helps you compare corresponding normalized values from multiple datasets to eliminate the effect of variations in the data set scale.

It makes it easy to compare data sets with small and large values. For example, if you have a data value of "2, 4, 6, 8, & 10," your normalized values for the first and last data points are zero and one, respectively. The middle point for the normalized value within the two is 0.5 as it's the mid-point. This formula also helps to compare multiple data sets with different scales. The formula for the normalization technique is:

Normalization (X new) = (X – Xmin) / (Xmax – Xmin)

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What is the purpose of the normalization formula?

Here are some of the major uses of the normalization technique:

  • Scaling down: The normalization technique is an important tool you can use to create a common scale to compare data sets with varying values. It's instrumental in a wide range of fields like ratings, where professionals use it to adjust the values that they measure on different scales to a notionally common scale.

  • Computing complex functionalities: You may also use it for more complex and sophisticated functionalities. For instance, aligning the entire set of a probability distribution of adjusted values or converting them to a quantile normalization where the quantiles of the different measures remain aligned.

  • Grading exams: Alternatively, exam companies and teachers may use the normalization technique to grade exams with questions of varying difficulty and align the scores to a normal distribution. The technique is useful as it helps distribute scores evenly across a range and compensate students with exams that contain more difficult questions.

  • Data mining and processing: Again, professionals may use this technique to process or mine data. You may also use this formula when your data set contains known upper and lower limits, and data remains evenly distributed across the range.

  • Prediction modelling and forecasting: Professionals also use it for forecasting, prediction, and modelling. They prefer to use this formula for these functions to make data models user-friendly and more relevant.

How to use normalization technique

Here are the steps to take if you wish to use the normalization technique:

1. Calculate the range in the data set

The first step in calculating the range of a data set is to find the minimum and maximum values within the set. You can easily do this when you arrange the values in your data set in ascending or descending order. Then subtract the least from the highest value. For example, a scientist wants to analyze a data set using the normalization technique. The results of multiple experiments are 12, 26, 28, and 32. The largest data point is 32, and the least is 12. Using the formula, the range for this data set is 20.

2. Subtract the minimum value from the data point value

The next step in using the technique is to subtract your range from the data point you're analyzing. You may begin with any data point within your data set. For example, the first data point in the scientist's data set is 25. Then, subtract the minimum value 12 from it to give you 13.

3. Insert the values into the formula and divide

Finally, divide the difference between the minimum value and specific data point by the range. This step means taking the result from step two and dividing it by step one. In the example above, you divide 13 by 20, resulting in 0.65. This result follows the normalization techniques as the value falls between zero and one.

4. Repeat process with additional data points

It's important that you apply the formula to each data point to analyze data sets properly. It's also useful in comparing data points within the set. Alternatively, you may automate this process using a spreadsheet program and save time instead of calculating manually. For example, after completing the first analysis using the normalization technique, you may conduct the same for the other data points to give results of 0, 0.8, and 1, respectively.

Related: How to Calculate the Median of a Data Set in Statistics

Reasons for normalizing data

The reasons for applying the normalization technique include:

To understand and assess a data range

The normalization technique allows you to reduce a wide range of data into figures that are easy to comprehend. For instance, you may wish to normalize a list of math scores for 50 students with varying results normally ranging from zero to a hundred. Normalizing these figures reduces the scores to decimals between zero and one such that you represent the lowest score of 20 as 0.2 and the highest score of ninety-nine as 0.9.

To compare different data sets with different data ranges

You may also use the normalization technique to better understand different data sets by establishing a relationship between them. For instance, you may wish to compare mathematics test scores with physics scores to identify the most and least successful students across both subjects. It's also possible that while you score the math test out of 100, the physics score is 50. Although the ranges are different, normalizing them places the scores on a balanced scale such that student who scores 80 in math and 40 in physics gets a uniform rating of 0.8 within a zero to one range.

Normalization technique for custom ranges

Although the normalization technique places all the results in a data set between zero and one, you may vary the formula such that the values fall within a custom range. For instance, you may customize your calculations such that the result ranges from zero to five instead of zero to one. This technique is ideal for computing data on a standard scale of one to ten, percentages, or scoring exams. The formula you may use is:

X normalized = a+ = ( ((X- minimum) * (b-a)) / range of X)

Similar analysis techniques in statistics

Asides from the normalization technique, other techniques that scientists use to modify and analyze data sets for other purposes are:

Feature clipping

This formula is the process of removing data points that fall outside a specific maximum or minimum value. Scientists use this formula to remove outliers and extreme figures that may skew the computation results in the data set. For instance, when scientists study orbiting items on a planet, they may remove the item that orbits outside a set distance. This step ensures that they include items orbiting that particular planet and not random items.

Z-score

Scientists use the Z-score normalization in machine learning to tell the distance between the data set average and the specific data point. It's useful in providing an easier way to compare data points with the norm when there are a few outliers in the data set. You may also use it to compare data sets that are likely similar due to experimental or genetic causes, such as results within a specific time frame or similar physical attributes of an animal.

Log scaling

Log scaling uses logarithms to compress wide ranges into smaller ones. It reduces the distance between the former data set and the later one as the scaling down may not be proportional. This method is most appropriate when measuring different natural occurrences like the brightness of stars.

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Normalization vs. standardization

Normalization and standardization are similar ideas, but they have some important differences. Normalization is the process of normalizing a range of data. It's the series of processes that scientists use to achieve scales between one and zero. This technique also places data points within the data range to the maximum and minimum range. Alternatively, standardization uses standard deviation to represent the distribution of data points. It also relates the data point to the average or the mean of all the data points.

For example, calculating a z-score is a standardization process as you can outsize the results out of the range of one to zero. Again, while a normalization technique converts values in a data range to fit into a certain range, more often one to zero, standardization transforms the same values to fit into a distribution that contains mean zero and standard deviation one. You may call this process mean centring or calculating Z-scores.

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