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Basic statistics. Mean and median

09/04/2026

The online basic statistics simulations on this page will help you to better understand the concepts involved in this important part of mathematics and in particular will help you to better understand what the statistical mean and median are.

What is statistics

Statistics is the branch of mathematics that allows us to understand and analyze data in the world around us. From economics to medicine to science and technology, statistics plays a fundamental role. Thanks to statistics, we know how to collect, organize, analyze and interpret data. It allows us to extract meaningful information from a set of observations. From opinion polls to scientific studies, statistics are everywhere.

Two of the most important statistical parameters are the mean and the median.

The Statistical Mean

The mean is the average value of a set of data. To calculate it, we add up all the values and then divide that sum by the number of values. For example, if we have the ages of five people (25, 30, 40, 40, 60 and 95), the mean would be:

Mean = (25+30+40+60+95) / 5 = 50 years.

The Statistical Median

The median is the value that is right in the middle of a set of ordered data. If we have the same ages as mentioned above, the median would be the value of the third person (40 years). If we had an even number of ages, we would average the two middle values.

Why are the mean and median important?

The mean and median help us understand the central tendency of our data. The statistical mean is sensitive to extreme values (such as a multimillionaire in a group of people with low income), while the statistical median is more robust to these outliers.

In short, statistics allow us to make informed decisions, understand patterns, and discover hidden relationships in data. The online statistical simulations on this page are an excellent tool to delve deeper into this important branch of mathematics.

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Basic statistics simulations

Mean: share and balance


This online simulation concentrates on explaining the concept of statistical mean. See how it is constructed and how the values of a statistical variable are distributed around it.
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Center and variability


This online simulation will help us to understand the concepts of statistical median and mean. With several exercises we will see how to obtain the value of these two important statistical parameters and how the values are distributed around them.
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Projectile Data Laboratory


Explore how statistics can shed light on the behavior of physical phenomena with this projectile launch simulation. Collect real data about launches—such as time, distance, and final velocity—and observe how they vary. Analyze the resulting sets by applying measures like the mean and median, and reflect on how these figures summarize and characterize the variability of data in real contexts of motion.
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Sampling distributions of projectiles


Dive into the connection between statistics and physics with this projectile sampling distribution simulation. Watch in real time as multiple launches generate different sample distributions, and see how, as sample size increases, those distributions converge toward a more expected shape—a visual illustration of the Central Limit Theorem in action. Use the generated data to calculate and compare measures like the mean, median, and deviation, and understand how these statistical tools describe datasets in real-world contexts.
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Test your knowledge

Statistics is the branch of mathematics that focuses on collecting, organizing, analyzing and interpreting data to extract meaningful information. It is fundamental in science, economics, medicine and technology because it allows researchers and professionals to understand patterns, evaluate hypotheses and make informed decisions. Measures such as the mean and median help describe the central tendency of a dataset. The mean represents the average value, while the median identifies the central value when the data are ordered. These tools allow us to detect trends, identify outliers and understand the structure of the data. Statistics transforms raw information into knowledge that can be used to explain phenomena, predict outcomes and support decision‑making.
The mean is calculated by adding all the values in a dataset and dividing by the total number of observations. It provides a global measure of the dataset but is sensitive to extreme values. The median, on the other hand, is the middle value when the data are ordered. If the dataset has an even number of values, the median is the average of the two central ones. The median is more robust when the distribution is skewed or contains outliers. Together, mean and median offer complementary perspectives: the mean reflects the overall magnitude of the data, while the median shows the central position. Comparing both helps identify asymmetries and understand the distribution more accurately.
It helps us make sense of large amounts of information. Whenever we have many numbers —grades, prices, temperatures, survey results— statistics allows us to organize them and find patterns. It helps calculate averages, identify common values, detect unusual data and make predictions. For example, analyzing daily temperatures can show what the typical weather is like and whether there were unusually hot or cold days. Statistics is used in science, business, medicine and almost any field that works with data.
The mean is the average: you add all the values and divide by the number of data points. The median is the middle value once the data are sorted from smallest to largest. The key difference is that the mean can be strongly affected by very large or very small values, while the median is much more stable. That is why the median often gives a better idea of the “typical” value when the dataset contains outliers.
Because it is not influenced by extreme values. If most people in a group earn between 1,000 and 2,000 euros but one person earns 50,000, the mean will increase a lot and give a misleading idea of the group’s income. The median, however, will show the true central value. This makes it especially useful in studies of income, housing prices and any situation where outliers distort the average.

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