What is statistics?
Definitions, real-world examples, and everything you need to know to excel in statistics.
Author
Tess Loucka
Published:
April 2025
Key takeaways
- • Statistics is the area of math that deals with collecting, organizing, analyzing, interpreting, and presenting data.
- • Descriptive statistics involves displaying and explaining data, while inferential statistics involves making predictions about populations based on sample data.
- • Mean, median, and mode measure the central tendency of a data set, while range, variance, and standard deviation measure data distribution.
Did you know that only 11% of the world’s population is left-handed?
Or how about this: 66% of a cat’s life is spent sleeping. For humans, that number is only about 33%!
Another interesting piece of information is that white cars are the least likely to get into an accident.
How do you think these tidbits were figured out? Someone didn’t ask every single person in the world whether they are left-handed or right-handed. Nobody has timed the exact number of minutes a cat sleeps during its lifespan. And it would be impossible to figure out the color of every car in every car accident worldwide.
So, rather than these being facts, these are examples of stats or statistics!
What is a statistic?
Statistics are conclusions drawn from data sets that tell us something about the world around us. Statistics allow people to draw conclusions from small sample groups about larger populations, leading to fun bits of information like the ones above!
But how exactly does statistics work, and what do you need to know to ace your statistics class?
What is statistics?
The subject of statistics relates to data, samples, and populations, but what is statistics really?
Statistics is a field of mathematics that deals completely with data. Any collection of data—whether it be from a science experiment or a class survey—can be better understood using statistics.
Statistics helps with collecting, organizing, analyzing, interpreting, and presenting data.
Statistics was originally created as a “state” science. It was used by the government to keep track of the population, economy, military, etc., but has since become a worldwide skillset that can be used in many areas of math and science, including psychology, sociology, chemistry, geology, political science, and more.
Basically, statistics is the measurement of two things within a data set: central tendency and dispersion.
Central tendency is thought of as the typical value within a data set. We use things like mean, median, and mode to calculate central tendency.
Dispersion is the way data is spread out (or dispersed) within a data set in comparison to the set’s average. To calculate this, we use standard deviation and range.
Understanding the statistics meaning is key to working with data in and outside the classroom!
Table of contents
Is statistics hard?
Basic statistics is introduced to students in middle school. In high school, students are expected to learn more complex statistics, often spending a full year or more on the topic. It can feel like a big change for students used to studying algebra and geometry as it is more closely related to probability than anything else.
Although statistics is a regular topic in the Common Core curriculum, it has a reputation for being hard. But is statistics hard?
If you’ve ever designed a survey, made a questionnaire, conducted a science experiment, or collected information on a group of people or things, you’ve worked with data before. Therefore, you know the basic rules of statistics!
Statistics simply takes data collection and analysis one step further, helping students better understand information and draw conclusions about their data.
Statistics may be difficult to some, but with enough practice, every student can excel! If you want to strengthen your statistics skills, devote a little time each day to studying and completing practice problems. You can find detailed statistics practice in DreamBox’s math program or by searching for textbooks and online resources.
Types of statistics
There are two main types of statistics. Let’s review them!
- Descriptive Statistics
This type of statistics is all about displaying data. There are many ways you can display data, including bar graphs, pie charts, line graphs, scatter plots, histograms, and tables. But data display doesn’t stop there—you can display data in more creative ways as well, such as through drawings or videos.
Descriptive statistics simply helps describe data and display it so that mathematicians or scientists can understand it.
- Inferential Statistics
This type of statistics is about interpreting data and drawing meaning from it. Once a conclusion about a data set has been made, it can then be used to make inferences about related populations.
For instance, the most common breed of dog on your street may be a good representation of the most common dog breed in your neighborhood.
The process of inferential statistics usually starts with collecting data from a sample population, analyzing the data, and then using that analysis to deduce information about the larger population the sample originally came from.
Statistics examples
Statistics is used in so many different ways, whether it’s in the classroom, the government, the doctor’s office, or a tech company start-up. There are endless ways statistics can be used to help us understand the world around us, but here are some common examples of statistics in real life:
Statistics in the classroom
- Correlation between test scores and time studying
Statistics can be used to analyze the relationship between the test scores of a class and how much time a student spends studying. You can use this data to determine the best amount of study time for achieving the best grades!
- Average class grades
You can use statistics to determine what the average grade is for the students in your class. Using mean, median, or mode, you can calculate the central tendency (average) grade and compare it to your own. Are you above or below average? Or are you right in the middle?
Statistics in sport
- Likelihood of your favorite team winning
By collecting and analyzing data, you can determine whether your favorite team is most likely to win or lose their next game! That way, you can emotionally prepare ahead of time for a big victory or loss.
- Player statistics
If you ever hear sports announcers talking about the “stats” of a player, they’re talking about statistics! A baseball player’s average pitching speed is really the mean speed taken from the data of all their previous pitches. A football player’s passer rating is their average passing success based on their previous passing attempts, completions, yards, interceptions, and touchdowns.
Statistics in daily life
- Expected traffic
The map app on your phone or computer uses statistics to calculate and infer how much traffic there will be on any particular route. Using a mix of inferential and descriptive statistics, you can optimize your daily commutes!
- Budgeting and managing your finances
You can use inferential statistics based on one month or two months of your income to predict how much you’re likely to make within a year, allowing you to budget for food, fun, and travel.
Statistics formulas
Before we get into the most common statistics formulas, let’s review some mathematical terms you should know first. Statistics uses terms that most students are not familiar with, and understanding what they mean is key to understanding bigger concepts in the subject.
Mathematical terms in statistics and what they mean:
- Σ – “The sum of all data set values”
- N – “The population size”
- n – “The sample size”
Many different formulas can be used in statistics, but there are seven main statistics formulas you’re likely to come across the most.
Mean
The mean of a data set is its average value. There are two types of mean in statistics: population mean and sample mean. Both are calculated the same, but population mean is the mean of an entire population while sample mean is the mean of a specific portion (or sample) of a larger population.
Sample mean (X̄) formula: (sum of all values in the data set) / (sample size)
X̄ = (Σ xi) / n
Population mean (μ) formula: (sum of all values in the data set) / (population size)
μ = ( Σ X i ) / N
Both formulas say that statistical mean is calculated by dividing the sum of all values in a data set by the total number of values in the data set.
Range
Range is a simple way to determine the spread or variation of a data set. Range tells you how much variety a data set has. For example, a data set of [1, 2, 3, 4, 5] has much less variety than [-5, 0, 5, 10, 15]—range can help define exactly how much variety there is.
To find the range of a data set, subtract the smallest value in the data set from the largest value.
Range formula: Range (X) = Max (X) – Min (X)
Variance
Variance is a more complex measurement of dispersion within a data set. It measures how far apart each value within the data set is from the data set’s mean.
Sample variance (s2) formula: sum of (every value in the data set – sample mean)^2 / sample size – 1
s2 = Σ (xi – x)2 / (n-1)
Population variance (σ2) formula: sum of (every value in the data set – population mean)^2 / population size
σ2 = Σ (xi – μ)2 / N
Standard deviation
Standard deviation is another measurement of data set dispersion. It is more commonly used than variance, and it measures how spread apart the values within a data set are.
To calculate standard deviation, just take the square root of the variance.
Sample standard deviation (s) formula: the square root of the sum of (every value in the data set – sample mean)^2 / sample size – 1
S = √1n−∑ni=1(xi−¯x)2
Population standard deviation (σ) formula: the square root of the sum of (every value in the data set – population mean)^2 / population size
σ = ([Σ(x – u)2]/N)1/2
Conclusion
There are countless things you can do with statistics, but understanding its basic principles and formulas is the first step. An interest in statistics can lead students to a life in meteorology, market analysis, data analysis, political science, sociology, economics, data science, and so much more.
It may seem tricky at first, but with time and effort, every student can find success in statistics!
FAQs
Statistics is the collection and analysis of data.
Descriptive and inferential statistics are the most common types of statistics, while exploratory data analysis is a third, less common type.
The five most basic statistical measurements are mean, median, mode, range, and standard deviation.
Much of statistics relies on mathematical calculations and analysis of numbers and data sets. A strong understanding of algebra is recommended for basic statistics and calculus for advanced statistics.
Statistics helps mathematicians and scientists gather, organize, analyze, interpret, and present data.
Statistics examples in real life include finding the average grade of a class, predicting the amount of traffic along a specific route, and calculating the likelihood of rain.
