How can normalize data

Normalizing or standardizing is an essential step in analyzing large datasets. Finding the z-scores of a sample data based on the standard deviation and mean of the entire data set can help you achieve a more manageable workload.

This is especially true for when comparing various sets of data. In this article, we are going to show you how to normalize data in Excel. Download Workbook. When we make the calculation we get the scores like this:.

To crosscheck the calculation, we can make graphs and see the line graphs of both columns have the same trends but different ranges. For example; we have a list of Math exam and Physics exam scores and we want to compare who is more successful on what. However; the Math exam was scored out of and the Physics exam was scored out of Since the ranges are different, the assessment out of original numerical values may be confusing. When we normalize the scores, we get:.

When we make graphs from both original scores and normalized scores , we see that original data is misleading because, for example, Jason looks like he is better at Math, however actually he is better at Physics. For instance; we have a portfolio of 8 stock exchange accounts with a mean of 23,5 and a standard deviation of 22,1. When we standardize the values, it is much more convenient to read and evaluate:. Standardization tells us the standard deviation of the value from the mean.

If a value has a negative standardized value, it means its value is less than the mean. Conversely, if a value has a positive standardized value, it means its value is bigger than the mean. All the other data points have decimal values between these two, in proportion to where that data point is within the range of the data set.

Example: If a data set had values of 2, 4 and 6, the normalized value of the first data point would be zero, the normalized value of the last data point would be one and the normalized value of the middle data point would be 0. Normalization is useful in statistics for creating a common scale to compare data sets with very different values. This normalization formula, also called scaling to a range or feature scaling, is most commonly used on data sets when the upper and lower limits are known and when the data is relatively evenly distributed across that range.

Professionally, data analysts may use a normalization technique to mine or process data. It can also be useful for prediction modeling and forecasting.

Some teachers and exam companies use normalization to grade exams when the questions are of varying difficulty, since the normalization process can distribute scores more evenly over a range and compensate for exams that may have more difficult questions. Here are the steps to use the normalization formula on a data set:. To find the range of a data set, find the maximum and minimum values in the data set, then subtract the minimum from the maximum.

Arranging your data set in order from smallest to largest can help you find these values easily. Here's the formula:. Example: A scientist is using the normalization formula to analyze a set of data.

They did their experiment four times, and their results were 12, 26, 28 and The largest data point in the set is 32, and the smallest is Next, take the x value of the data point you're analyzing and subtract the minimum x value from it.

You can start with any data point in your set. Example: The scientist's first data point is 25, so the scientist subtracts the minimum x value from that:. So scale by 90, then add That should be enough for most of the custom ranges you may want. Show 5 more comments. I mean, is there an "original" reference somewhere? Show 1 more comment. Nick Cox That explained the main idea clearly and directly and then secondarily showed how to do it in one commonly used program. Conversely, you post here only code.

While I am happy to believe that this is good code I don't write PHP on this forum we don't normally have a bundle of answers to every question explaining how to do it in every conceivable language. Python, etc, etc. In my code, I also showed, how to return a normalized value to the value it was before normalisation. I think, that makes it worth this answer. Presumably inverting the scaling is of use only when a the original values have been overwritten but b the user has prudently remembered to save the minimum and maximum.

My wider point, as commented above, is that CV does not aim to be a repository of code examples. But you're right, in manner of data analysis, this answer is very bad. I just think the answer is off-topic therefore. Isn't it better all 0. All items are equal, so should be kept centered in the interval.