You might have dealt with summation in mathematics from school, college, and university. Even if you are not a math student, you may still be familiar with this concept. This is because it is an integral part of many other subjects, such as physics, statistics, finance, etc.
However, have you ever wondered whether summation is just limited to books or is it applied in real life? If this type of thought usually comes to your mind, then fortunately, you are at a place where your confusion will be cleared. Yes, you heard it right.
In this article, we will walk you through some applications of summation in different fields. However, before that, let’s first recall its definition, notation, and other basic things about it.
What Is Summation?
Summation is an essential mathematical operation just like addition, division, subtraction, and multiplication. It usually refers to summing up a sequence of numbers. Many people confuse it with simple addition, which is not right. Remember, the thing that differentiates summation from addition is that it involves large series, not just two or three numbers.
It is usually represented by a symbol Σ that indicates the sum over a specific range of sequences. It is specially used when we deal with functions. However, it can also be applied to integers and decimals.
Applications Of Summation In Different Fields
Let’s look at where summation is applied in real life and how it contributes to making life easier.
Business Finance
Summation plays a significant role in business finance, especially in estimating expenses and sales. It allows companies to plan for their yearly expenses over a defined range. Also, it enables them to sum up the individual sales to find the total revenue generated. This helps them to make informed decisions regarding how much budget they need to dedicate for annual expenditure. Additionally, it makes them capable of determining whether the sales revenue meets their expected numbers or not.
Data Analysis In Statistics
If you belong to statistics, you may know that many statistical measures are dependent on the summation. Whether it is the calculation of variance or standard deviation, it serves as an integral component in their formulas. For instance, summation is used with the square of the difference between ith point and the mean of all points in a dataset when calculating the standard deviation. This allows experts to make accurate predictions from collected data. This is just one example of the involvement of summation in statistics.
Economics
Whether it is calculating demand and supply in the market, summation helps in both cases. It allows economists to track stock performance by adding up the values of production cost and purchase cost over time. The analysis of aggregation of price changes helps them in the calculation of inflation rates. All these things together help them to make the right economic decisions. As a result, they manage to keep the market stabilized and avoid any unwanted financial issues.
Physics Calculations
Another field where summation has practical implementation is physics. Many real-life experiments involve the sequential addition of physical quantities. This is where summation comes in to simplify the problems. The most prominent example of its use in physics is the calculation of work done when a variable force is applied. In this case, it helps researchers to add up small amounts of work done in each interval. Apart from that, it is also utilized to find out the kinetic energy of a system of particles where thousands of particles are involved.
Programming
Being an important part of computer science math, the summation is also applied in programming. Programmers use it in loops to calculate totals. It helps them to add values in a list and count the occurrences of certain events. Moreover, it also aids them in determining the cost of loop execution in programs, especially in those in which the algorithm contains many loops. It is not just part of traditional programming, but it is also being used in modern AI algorithms to make codes more efficient and reliable.
How To Calculate Summation?
Calculating summation may seem easy, just like addition, but it’s not. Summing series with short limits may be just a few steps game, but the real problem arises when you deal with large sequences. In this situation, you have to delve into lengthy and complex calculations, and the complications may increase if more sophisticated functions are involved.
That’s why adding up larger or more complicated sequences requires a more advanced solution, such as a summation calculator. You just have to enter the function and limits to the tool, and it automatically performs accurate summations within seconds. This not only saves you time and cuts your efforts but also eliminates the chances of inaccuracies in results.
To Sum Up
To put it in a nutshell, summation is applied in many fields such as statistics, business finance, physics, and computer science. We hope that its diverse application has helped you to understand its importance in real life.
