Statistical index, a strategic tool for our analyses
How to extract a lot of information from data
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“Mom, look at that beautiful hat!” When I was a child, I would say this to my mother whenever I saw something beautiful. I would point to it with my finger. “Don’t do that. Don’t point. It’s not polite,” she would reply.
But how could I show her the most beautiful hat on the beach without pointing? I would have had to describe it in words.
Yes, that would certainly have been polite, as she said. But, by then, the girl wearing it would have gone away. My mother would have missed the chance to see the hat that I wanted her to buy for me, too 😊
How can you describe a complex situation in a simple way?
When we were young, pointing with our index finger at an object, toy, or character was the most natural way to show someone something. The name of this finger likely comes from its original use.
It was our fast and effective way of communicating.
Not doing so meant describing the object in detail with words. This would have wasted a lot of time and not conveyed the idea as fully as observing the image directly.
Even as adults, we often find ourselves describing situations, events, or phenomena that are actually very complex. This may be because they have many different facets, or are the result of many different factors, or are the evolution of a phenomenon that originally presented itself differently.
In short, reality is often too complicated to be immediately described or understood with a simple image or text.
Fortunately, in the scientific field, there are tools to help us solve this problem. These are called indices or indicators.
How do they do it? They do this by expressing a number.
Yes, you got it right!
An index is just a number, sometimes shown as a percentage (%), that sums up a lot of information in one data.
An index is worth a thousand words
You may already be familiar with this concept. It is so common and a part of our everyday language that we often use it without even realizing it.
For example, we often hear about approval ratings, audience ratings, humidity levels, and smog levels in cities. These are just a few examples of indices that we commonly use.
Thanks to indices, we can analyze and evaluate a single phenomenon in many sectors in absolute terms without taking specific values into account and understand its overall scale.
For example, let’s take television share. In summary, it indicates how many viewers are watching a particular program. It does this by taking into account the total number of people watching TV during that time.
How does it do that? It divides the number of viewers of a program by the total number of people watching television at that moment. Then, the result is multiplied by 100.
Simple, then. An index is a ratio. A mathematical division between two quantities of the same kind, referred to in mathematical jargon as homogeneous quantities.
In our example, the divided quantities represent the spectators:
Share: The number of viewers watching a specific program divided by the total number of people who turned on their TVs.
Market Indexes
Many fields use indexes. These include not only science, but also economics, finance, the social sciences, politics, and more. They use them to express aspects of real situations that are often too multifaceted and complex.
As a quant, I work with many indices. One category is financial indexes. These are designed to represent an entire sector, such as a specific stock exchange or a particular region of the world. They summarize this sector with a single value. This value must immediately convey the sector’s current situation. They also allow us to understand how they have changed over time.
The idea behind creating a financial index is to select the most relevant data for the sector you want to study. Then, you combine them in a logical and meaningful way, such as by calculating a simple average. In reality, however, it is more complex than that.
A practical example is the DAX (Deutscher Aktien Index), which is the primary stock index of the German stock exchange. The DAX consists of 40 German stocks listed on the Frankfurt Stock Exchange that are selected based on their market capitalization and liquidity. These stocks can belong to either the traditional or technology sectors.
For this reason, the DAX 40’s value provides a snapshot of the German economy’s performance.
The benefits of using an index
The main benefits of indices are:
– Allow for comparison with other indicators representing different realities, such as product sector or geographical area
– They help evaluate the evolution of a phenomenon over time
– They also allow estimates to be made about the trend of the phenomenon they represent
What is important to understand is that they are strategic indicators for our analysis in any field we work in.
But how can we determine which one is right for our assessments?
There may not be a “ready-made” index that can translate and summarize what we want to analyze. In this case, we would need a customized index that meets our specific needs.
You won’t believe it, but it’s possible! Yes, you heard right. You can create your own personalized index and choose the information you want to work with to achieve your desired result.
However, the process is quite lengthy. Explaining it would require more pages than a blog article can provide, and it would take too much time to read. If you are interested, though, I can tell you that my book Value Investing with Excel has an entire section dedicated to the importance of indices and techniques for creating them.
If you’re curious and would like to learn more about this topic, click the button below…
Remember, you can also create your own personalized index if you want!
Post published on 08/07/2025 by Donata Petrelli on site https://www.donatapetrelli.com
Title Image credits and copyrights by Ilya Mazurkevich on StockSnap
