Basic statistics. Mean and median
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.
This Thematic Unit is part of our Mathematics collection
STEM OnLine mini dictionary
Absolute Frequency
The number of times a specific value or response occurs within a data set.
Arithmetic Mean
The average value of a set of numerical data, calculated as the quotient of the sum of all values and the total number of data points.
Data Distribution
The way the values of a variable are organized and spread, allowing for the identification of patterns and trends.
Median
The central value of an ordered data set that divides the sample into two equal parts, with 50% of the data above and 50% below.
Mode
The value or category that appears most frequently within a data distribution.
Outlier
A numerical observation that lies significantly far from the rest of the data, potentially distorting the arithmetic mean.
Population
The entire set of individuals, objects, or events that share a common characteristic and are the subject of a statistical study.
Sample
A representative subset selected from a population upon which statistical observations and measurements are performed.
Statistical Range
A measure of dispersion indicating the difference between the maximum and minimum values of a distribution.
Statistics
The branch of mathematics that develops methods for collecting, organizing, analyzing, and interpreting data to draw valid conclusions.
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.
STEM OnLine mini dictionary
Absolute Frequency
The number of times a specific value or response occurs within a data set.
Arithmetic Mean
The average value of a set of numerical data, calculated as the quotient of the sum of all values and the total number of data points.
Data Distribution
The way the values of a variable are organized and spread, allowing for the identification of patterns and trends.
Median
The central value of an ordered data set that divides the sample into two equal parts, with 50% of the data above and 50% below.
Mode
The value or category that appears most frequently within a data distribution.
Outlier
A numerical observation that lies significantly far from the rest of the data, potentially distorting the arithmetic mean.
Population
The entire set of individuals, objects, or events that share a common characteristic and are the subject of a statistical study.
Sample
A representative subset selected from a population upon which statistical observations and measurements are performed.
Statistical Range
A measure of dispersion indicating the difference between the maximum and minimum values of a distribution.
Statistics
The branch of mathematics that develops methods for collecting, organizing, analyzing, and interpreting data to draw valid conclusions.
Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!
Basic statistics simulations
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.
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.
Giants of science
“If I have seen further, it is by standing on the shoulders of giants”
Isaac Newton
Carl Friedrich Gauss
–
Blaise Pascal
–
Become a giant
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Giants of science
“If I have seen further, it is by standing on the shoulders of giants”
Isaac Newton
Kurt Gödel
–
Blaise Pascal
–
Become a giant
Probability and Statistics in Data Science using Python
Introduction to Probability
Fundamentals of Statistics
Fat Chance: Probability from the Ground Up
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Introduction to Algebra
Maths Essentials
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Test your knowledge
What is statistics, and why is it essential for analyzing data across different fields?
How are the mean and median defined, and what role do they play in describing central tendency?
What is statistics used for in everyday life?
What is the difference between the mean and the median?
Why is the median sometimes more useful than the mean?
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