We often encounter dilemmas involving both quantitative and qualitative factors. Mathematics plays a key role in decision-making by helping us to evaluate and improve the quality of the information in the presence of uncertainty. Different branches of mathematics such as algebra, statistics, optimisation, probability, mathematical induction, modelling, and many others are crucial to the decision-making process in various places, right from businesses, manufacturing, finance, law, public policy, health, to the mundane daily activities.
Our decisions are usually based on quantitative and qualitative factors. Also, the Mathematical Induction of Class 11 Maths is based on deductive reasoning. This is also helpful in decision making. The following factors should be kept in mind while making any decision.
Mathematical Models are based on abstraction for example 1 apple + 1 apple = 2 apples which implies every apple is an identical object. But one apple can have worms in it. Also, have qualitative differences like color, taste, smell, texture, and many more. Qualitative properties can be sensed by human senses whereas qualitative properties like mass, chemical composition and many others required mathematical or scientific measurements.
Mathematical models are based on assumptions. Assumptions made in mathematical models can streamline the decision-making process, but if they are not accurate, they may result in incorrect decisions.
When using Maths to make decisions, it is important to consider and account for uncertainty by asking "What if?" and calculating over a range of foreseeable values. Taking a safer option with lower potential value may be a better decision in some cases.
Mathematical models will only provide information on what is specifically asked of them, so it is crucial to ensure that the correct factors are being measured.
It is important to take into account the emotional and human elements when assessing value, as ignoring these factors may lead to important variables being omitted. Personal emotions and preferences can also play a role in determining the best decision, even if it may not be the most logical choice.
Understand With Examples
Suppose there is a small box of chocolates of 5kg which costs ₹ 2500. Also, there is another larger box that has 10kg and costs ₹ 4500. Which box should I buy?
Quantitative
This type of analysis required scientific measurement. using mathematics we can do a calculative analysis that the small box costs ₹ 0.5 per gram, while the larger box costs ₹ 0.45 per gram. Quantitatively purchasing a larger box is good.
Qualitative
This type of analysis is judged with the human senses. we can do a qualitative analysis basis on the space it will take and the convenience to carry the box. Generally, small and slim objects are easy to carry.
The decision will depend! Do I have sufficient free space or not? And how feasible to carry the box? Also, it depends on whether ₹500 is worth the lost space and inconvenience.
Here is another example. Let's consider the fact that I am going to purchase a car. There are two cars, which one should I buy?
Quantitative
Using mathematics I can do quantitative analysis. I can do comparisons on resale value, miles per gallon (MGP), storage space, etc. Also, I can compare the purchase price to the purchase price of "similar" cars to see if it is over/ underpriced.
Qualitative
Here we’ll consider "non-quantifiable" features for example five-star safety rating, heated seats, color, Bluetooth compatibility, and many more.
It depends! What are those features worth to me monetarily? Is it worth an extra ₹ 5,00,000 for added features?
Some people may focus heavily on quantitative data and neglect important qualitative factors, while others may focus too heavily on personal preferences and emotions and neglect important quantitative data. The key is to find the appropriate balance and use the appropriate Maths for the specific situation, while also considering other relevant factors. It's also important to not overlook the importance of other reasoning skills during decision-making. Now let's understand these concepts using financial investment which becomes part of daily life.
Financial And Economic Investment
Today’s youth is not just tech savvy, they are also very cautious about financial investments. They are absolutely comfortable with multiple platforms like stock trading, mutual funds, fixed deposits, government bonds, and sovereign government bonds. So for them, it is essential to understand how to make the right decisions. Maths can help to improve decision-making.
We can quantify the risk and expected return using mathematics tools. and make a balance between them.
Statistics measures the quality of information and optimization finds the best alternative.
Probability quantifies and manages uncertainty. Control automates decision-making.
Regression analysis can be used to analyse historical data and make predictions about future market trends.
Overall, Maths can help to make informed decisions in financial and economic investments. Following are some tips for students to improve their decision making using maths.
Tips To Improve Decision Making
Practice problem-solving: Students can practise Maths problems and puzzles that require logical thinking and decision-making. This habit really helps students to improve their decision making.
Learn decision-making strategies: there are multiple types of decision making strategies for example decision trees, Venn diagrams, mind mapping, and flowcharts. Students can practise these strategies so that they can apply in their daily life while making decisions.
Use data and statistics: Learn how to collect, analyse, and interpret data to make informed decisions. Statistics is very useful in daily life as we can calculate mean, median, mode, variance, standard deviation and many other statistical parameters. These are crucial to understand the data and help to do hypothesis testing.
Apply maths in real-life situations: Try to apply maths concepts to real-life situations, such as budgeting, planning, and forecasting.
Take a class: Consider taking a class on decision-making or statistics to learn more about the application of maths in decision-making.
Practice, Practice, Practice: Continuously practising what we have learned will help us to apply the knowledge in real-life scenarios, making better decisions.
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