Have you ever wondered how scientists make claims about millions of people by studying just a few thousand? Or how pollsters predict election results without asking every single voter? The answer lies in two powerful concepts: Descriptive and Inferential Statistics.
Let me show you exactly how this works with a simple question: What’s the average height of a human being?
Your first instinct might be: “Easy! Just measure everyone on Earth and calculate the average.” But here’s the problem there are over 8 billion people on this planet. Measuring everyone would take decades, cost billions of dollars, and by the time you’re done, the data would be outdated!
So here’s the smarter approach: What if we carefully selected a diverse group people from different continents, countries, cultures, and communities measured their heights, and used that to estimate the average for everyone? This isn’t just easier, it’s actually the foundation of modern statistics. And it introduces us to two fundamental concepts you’ll master today: Population and Sample.
By the end of this video, you’ll understand not just what these terms mean, but how they power everything from medical research to business decisions to scientific discoveries.
Let’s dive in!
Population
Is the entirety of the whole set of individuals, data points, objects or events that are the subject of interest in a given statistical study. In the example above, this is the whole number of all human beings on the planet Earth.
Sample
Sample is a subset of the population, a smaller, more manageable subset of individuals, objects, or events selected from the population to represent the whole population. In the example above, this would be all the people we selected from diverse countries, towns, cities, races, continents etc, that represent the larger population of all humans on Earth in our study.
We use samples in situations when we can not get data about the whole population, so we take a small part of the larger population which represents this larger population well.
Now, armed with this knowledge of the difference between a population and a sample, we can now go ahead and understand descriptive statistics and inferential statistics.
Descriptive Statistics
Descriptive statistics provides methodologies and tools to provide a description of the underlying sample in our study. Descriptive statistics is used to describe the sample. Example, what is the median height of all the people who were involved in our study, what are their age distributions etc.
Whatever statements we are able to derive from Descriptive Statistics is not a statement on the larger population.
NOTE
Some people argue that descriptive statistics is not always used on sample data and can be used on population data as well. I agree with this, imagine you are conducting an experiment amongst your family members that you can get access to and collect data from each person. The whole family is your population, hence the data you collect is population data, not sample data.
You can think of this in another level, you are a student at a university and you want to find the average score of a certain module of a course. You can go to the university administrators and get the unanonymized grades for each student of that module, hence that data is a population data, not a sample data.
In descriptive statistics, we have methods and techniques used to provide description of the data, for example using statistical characteristics like mean, median, variance, graphs and charts.
NOTE: No conclusions are known from descriptive statistics, unless the data collected includes the whole population.
Some of the methods or techniques used in descriptive statistics involves:
Location Metrics
These are used to explain what we call the central tendency of the data. This involve the use of statistical metrics like:
- Mean: Best for symmetrical (normal) distributions without extreme outliers.
- Median: Preferred for skewed distributions or when outliers are present (e.g., income data).
- Mode: Best for nominal data or when finding the most common observation is the goal.
Dispersion Metrics
This provides information on how data points in the sample differ from one another. It helps address questions like, how far are the data points from each other, are the data points close to the central point? We can use some of the listed methods below to answer these questions.
- Range
- Inter-quatile Range
- Standard deviation
- Variance
3. Tables
- Frequency tables
- etc…
4. Charts
- Pie charts
- Histograms
- Stem-and-leaf plots
- Bar chart
- Correlation matrix
Inferential Statistics
Inferential statistics on the other hand, allows us to make conclusive statements about the larger population. In more formal terms, inferential statistics is a branch of statistics that uses data analyzed from a small sample to make generalizations, predictions or inferences about the larger population.
Whatever statements we derive from Inferential Statistics is a statement on the largest population. The main goal of Inferential Statistics is to infer the UNKNOWN parameters and metrics of the larger population using the known information of the sample from this larger population.
Commonly used approaches in inferential statistics are t-tests, chi-square tests, hypothesis testings or analysis of variance (ANOVA).
Simple Test Methods
- t-Tests
- Chi-square test
- F-test
- etc…
Regression Analysis
- Simple Regression
- Multiple Regression
- etc…
ANOVA
- Single factorial ANOVA
- Two factorial ANOVA
- etc…
Conclusion
Congratulations for making to the end! And that’s it! You now understand population vs sample, and descriptive vs inferential statistics. Next up, we’re diving into levels of measurement. Thank you for reading and see you in the next article.
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Happy coding! And see you next time, the world keeps spinning.