Data & Mathematics
- neovijayk
- Jul 6, 2020
- 3 min read
In this post I will introduce some of the important terms and concepts in mathematics that you may encounter in your Data Science projects. As show in the following diagram data science is generally shown at the intersection of Mathematics, Computer Science and Domain Expertise or Subject Matter Expertise.
Dig: Generally accepted Data science description
Mathematics & Statistics
Mathematics is the abstract science of numbers, quantity and space. Mathematics may be studied in its own right (pure mathematics), or as it is applied to other disciplines such as physics and engineering (applied mathematics).
Statistics is the science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions as a whole from those in a representative sample.
Source: website
What does a Mathematician do?
Mathematicians solve problems. Problems they work on range from pure mathematical problems to applied problems.
Mathematicians try to find common features in seemingly distinct problems.
That is, they look for patterns. They classify what behaviors can result from certain systems.
For example, differential equations can be used to show that an electrical RLC circuit “behaves” in exactly the same way as a spring-mass system, oscillating back and forth until the motion damps out.
Graph theory can be used to schedule tournaments with scheduling constraints, or to show that certain scheduling constraints are impossible to meet.
Often studies which are considered at one time pure mathematics, with no application in mind, turn out to be the most useful. For example, pure research studying efficient factoring algorithms for large integers led to extremely useful algorithms for computer encryption.
Applied mathematicians use mathematical theory, computational techniques, algorithms and the latest computer technology to solve economic, scientific, engineering and business problems.
This process often involves building a mathematical “model” of the application,using mathematical theory to understand the behavior of the model, and then interpreting this behavior in the context of the original application.
Some applications include designing the most fuel efficient rocket path to the moon, advising the DNR how many deer licenses to sell, and predicting the effect of vaccinations on epidemics.
What does a Statistician do?
Statisticians develop techniques to overcome problems in data collection and analysis. They use statistical methods to collect and analyze data and to help solve real-world problems in business, engineering, healthcare and other fields. For example, they design medical experiments to make sure that valid conclusions can be drawn about the use of medications, they suggest marketing strategies based on relatively small samples of consumers, and they decide what premiums to charge on insurance policies.
What is statistical inference and why do we need it?
Statistical inference refers to the process of drawing conclusions from the model estimation.
Statistical inference is important in order to analyze data properly.
Indeed, proper data analysis is necessary to interpret research results and to draw appropriate conclusions.
For example in case of data about Population – Statistical inference is the process through which inferences about a population are made based on certain statistics calculated from a sample of data drawn from that population.
With this knowledge we will move to next important topics which I have divided them into following different sections:
Data and Statics
Measures of Central Tendency : Mean, Median, mode. (coming soon)
Measures of Position: Quartiles and Percentiles. (coming soon)
Measures of Dispersion: Standard deviation, range, and interquartile range (coming soon)
Data Distribution and Probability Distributions
Basics of Probability. Representation of data in Frequency distributions, relative frequency distributions. Also what is standard normal distribution? (coming soon)
Graphical Representation of Data
Graphical data representations, such as bar graphs, circle graphs, and line graphs, etc (coming soon)
(For more details please check this ScienceDirect link)
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