If, like most people, you have been wondering how the world works? How do we measure the amount of rainfall each year? Or what the average temperature is in a given country?
All these calculations and many more are possible through the power of statistics, as it helps us analyze data from experiments, surveys, or other sources in order to identify patterns or trends.
Statistics is a branch of mathematics that uses numerical data to analyze, interpret, and draw conclusions. Through statistics, researchers use data analysis and probability theory to draw conclusions about various phenomena.
This article will give a brief overview of the different types of statistics used in mathematics and how they are applied. You might also enjoy reading: Is AP Statistics Hard? An overview of what to expect!
What is Statistics?
Statistics is a branch of mathematics that focuses on developing and studying methods for collecting, analyzing, interpreting, and presenting empirical data (Source: The University of California Department of Statistics)
There are statistics applications in virtually all scientific fields. For example, individuals use statistics to make financial planning and budgeting decisions. And institutions, such as banks, use statistics to lower risk in lending operations, analyze financial market activity, and predict economic crises’ impact.
Statistics is generally used to determine how to draw reliable conclusions about large groups and general events from small samples’ behavior and other observable characteristics.
If you are a student looking to learn statistics, I encourage you to read this article, where I shared 9 helpful tips on how to understand statistics easily.
What Are The Different Types of statistics in Mathematics?
There are two types of statistics in mathematics: descriptive and inferential.
- Descriptive statistics describes sample and population data properties, including mean, variance, skewness, and kurtosis.
- Inferential statistics uses those properties to test hypotheses and draw conclusions.
Descriptive statistics are used to summarize a set of data points by establishing its central tendency (mean, median, and mode) and its dispersion (range, standard deviation). Generally, descriptive statistics focuses on summarizing and organizing the data so it can be easily understood (Source: Duke University)
In addition, descriptive statistics allow for quick visualization of data so that patterns can be identified quickly. This type of statistic is useful for reporting on large datasets as it allows for easy comparison between different sets.
Unlike inferential statistics, descriptive statistics are typically easy to interpret and aims to describe the data but does not try to make inferences or assumptions from the sample to the whole population.
Inferential statistics aims to discover some property or general pattern about a large group by examining a smaller group of people or objects, expecting the results to generalize to the larger group (Source: Purdue University)
In other words, inferential statistics allows us to use sample data from a population to make predictions about the larger population. The main goal here is to infer relationships between variables in order to make more accurate predictions about future events or behaviors.
For example, if you look at survey results from a small sample size within a particular city and find that people there prefer one brand over another, then you can make an inference about what the preferences would be among the entire population living in that city.
Unlike descriptive statistics, inferential statistics are usually complex and may have several interpretations.
The table below shows the key characteristics of descriptive and inferential statistics:
|Descriptive statistics are used for summarizing and organizing data in meaningful ways, which include measures such as means, medians, mode, range, variance, and standard deviation. By using these measures, you can summarize large sets of data into a more manageable form that can then be used for further analysis.
|Inferential statistics are used when conducting hypothesis testing in order to make inferences about a population based on sample data. These methods include t-tests, chi-square tests, and correlation tests, which allow researchers to determine how likely it is that their conclusions about the population are valid.
|Measures of Central Tendency
|– Standard deviation
– Interquartile change
– Mean absolute difference
– Median absolute deviation
– and Average deviation
|– Linear regression
– Nominal regression
– Ordinal regression
Bayesian statistics is an approach to inferential statistics that relies on probability models instead of frequentist approaches such as hypothesis testing or confidence intervals.
Bayesian Statistics takes into account prior information based on previous studies or experiences and combines it with new evidence when making predictions or decisions.
Bayesian statistics applies probability to statistical problems and provides mathematical tools to update or revise our beliefs about random events in light of seeing new data or evidence.
Bayesian Statistics is often used when there are unknown variables or when decisions need to be made without complete certainty due to limited data availability.
Statistics for Machine Learning
Recently, machine learning has become increasingly popular in many fields due to its ability to automate tasks that would otherwise be done manually.
As such, it has become important for statisticians to develop new statistical techniques specifically tailored for machine learning applications such as neural networks and decision trees.
The techniques used in statistics for machine learning involve using mathematical models such as regression models or Bayesian networks in order to make predictions based on given data sets.
Statistical modeling involves using mathematical models such as linear models or time series models in order better to understand the relationship between variables within a dataset.
Statistical modeling is often used by economists or financial analysts when trying to predict stock prices or other economic indicators over time.
It can also be used by scientists when trying to determine the effect of one variable on another within an experiment or survey setting.
What to read next:
- Should You Take Statistics or Calculus in High School?
- Is Elementary Statistics Hard? (Including how to make it easier!)
- 6 Reasons Why Statistics Is So Hard (And helpful tips for studying stats!)
- Is Statistics Harder Than Calculus? (Yes! and here’s why!)
Statistics is an essential tool for understanding complex phenomena. It plays an important role in understanding how our world works by helping us draw conclusions from numerical data.
Many different types of statistics can be applied depending on the situation at hand. From descriptive stats, which summarize large datasets, to inferential stats, which allow us to make predictions about populations, all the way up to Bayesian stats, which incorporate prior information into decision-making processes, statistics have become an invaluable tool in modern mathematics.
With these different types of statistics at our disposal, we have greater insight than ever before into how our world works and how we can better navigate it.
Whether you are a student looking for help with math homework or a business owner trying to understand customer behavior, I believe that understanding these different types of statistical methods will help you get closer to your goal.