What is Statistics? Definition, Meaning, Characteristics and Examples
When we hear the word Statistics, we often think of numbers, averages, tables, graphs, and percentages. That is certainly part of statistics, but statistics is much broader than simply calculating averages.
Statistics gives us a systematic way to collect, organize, present, analyze, and interpret data. It also helps us understand variation in data and draw conclusions when there is uncertainty.
For example, if the marks of 100 students are collected, the list of marks is only the starting point. We may organize the marks into a frequency table, represent them graphically, calculate the mean or median, study their variation, and then interpret what the results tell us about the students' performance.
So, statistics is not merely about doing calculations. It is about learning from data.
What Does Statistics Mean?
The word Statistics is used in two related senses.
1. Statistics as Numerical Data
In one sense, statistics refers to numerical facts or data.
Examples include:
- Population of a country
- Number of students in a college
- Annual sales of a company
- Unemployment rate
- Average rainfall
- Marks obtained by students
- Production of a factory
For example:
A college has 2,500 students.
The number 2,500 is numerical information about the college.
In this sense, statistics refers to numerical facts or aggregates of data.
2. Statistics as a Subject or Discipline
Statistics is also the name of the discipline that provides methods for working with data.
It includes methods for:
- collecting data,
- organizing data,
- presenting data,
- analyzing data, and
- interpreting the results.
In modern statistics, we also study sampling, probability, statistical inference, variability, uncertainty, and the quality of data.
This second meaning is the one we usually have in mind when we say:
“I am studying Statistics.”
A Simple Definition of Statistics
A useful modern definition is:
Statistics is a discipline concerned with collecting, organizing, presenting, analyzing, and interpreting data in order to obtain useful information and draw appropriate conclusions in the presence of variability and uncertainty.
For a beginner, this can be shortened to:
Statistics is the study of data and the methods used to collect, organize, analyze, and interpret it.
This simple definition is easy to remember, while the longer definition gives a more complete picture of the subject.
Modern introductory statistics texts similarly describe statistics in terms of the collection, analysis, interpretation, and presentation of data, while also emphasizing sampling, variation, and statistical inference.
Why are there Different Definitions of Statistics?
You may notice that different authors define statistics in different ways. There is a simple reason for this.
The meaning and scope of statistics have developed over time. Older definitions often emphasized numerical facts, counting, averages, or the condition of a state or society. Later definitions focused more on the methods used to collect, present, analyze, and interpret data.
Therefore, the older and newer definitions should not be treated as completely unrelated. Each one highlights a particular aspect of statistics.
Definition of Statistics by Different Authors
Quantitative or numerical information (data) could also be found almost everywhere in business, industries, economics and lots of other areas. Data in quantitative form is probably commonly referred to as statistical data. But not all numerical data is statistical and hence it's necessary to look at a couple of definitions of Statistics to know the characteristics of statistical data.
The following classical definitions are commonly discussed in college-level statistics.
1. Definition of Statistics According to Webster
Webster defined statistics as follows,
Statistics are the classified facts representing the conditions of the people in a State especially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.
What does this definition mean?
The definition emphasizes three ideas:
- facts,
- numerical expression, and
- classification or arrangement.
For example, information about population, births, deaths, employment, or production can be collected and arranged to describe the condition of a population.
Limitation of Webster's Definition
This definition reflects the older use of statistics and is relatively narrow by modern standards.
Statistics is no longer limited to facts about the state or government. Today, statistical methods are used in almost every field, including:
- Business
- Economics
- Science
- Medicine
- Education
- Engineering
- Agriculture
- Psychology
- Social sciences
- Industry
- Sports
- Data analysis
Therefore, Webster's definition is useful for understanding the historical meaning of statistics, but it does not describe the full scope of modern statistics.
2. Definition of Statistics According to Horace Secrist
Horace Secrist gave one of the well-known classical definitions of statistics.
By statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose, and placed in relation to each other.
In simple terms, Secrist described statistics as aggregates of facts that are influenced by multiple causes, expressed numerically, collected with reasonable accuracy and in a systematic manner for a predetermined purpose, and placed in relation to one another.
This definition is particularly useful because it tells us several important characteristics of statistical data.
Understanding Secrist's Definition
1. Statistics are aggregates of facts
Statistics generally deals with an aggregate or collection of observations, rather than one isolated fact.
For example:
The height of one student is 165 cm.
This is a single observation.
But:
The heights of 100 students are recorded and studied.
This gives an aggregate of observations that can be analyzed statistically.
2. Statistical facts are affected by multiple causes
Many statistical phenomena are influenced by several factors.
For example, crop production may depend on:
- rainfall,
- soil,
- temperature,
- irrigation,
- fertilizers,
- quality of seeds, and
- farming practices.
Therefore, statistical phenomena are often the result of several interacting causes.
3. Statistics are numerically expressed
Classical statistical data are generally expressed in numerical form.
Examples include:
- 75 marks
- 65 kg
- ₹50,000
- 12%
- 2.5 hours
Numerical expression makes comparison and statistical analysis possible.
4. Facts may be enumerated or estimated
Statistical information may be obtained by counting or by estimation.
For example:
- Number of students in a classroom → counted
- Estimated population of a city → estimated
5. Statistics require reasonable accuracy
Data should be collected with a degree of accuracy appropriate to the purpose of the study.
The required accuracy is not necessarily the same in every investigation.
For example, a laboratory measurement may require much greater precision than a rough estimate used for a general survey.
6. Data should be collected systematically
Statistical data should be collected according to a planned procedure.
For example, if a researcher wants to study household income in a city, the researcher needs to decide:
- what population is being studied,
- how households will be selected,
- what information will be collected, and
- how the information will be recorded.
7. Data are collected for a predetermined purpose
A statistical investigation should have a clear purpose.
For example:
A school collects students' examination marks to study academic performance.
The purpose of collecting the data is clear.
8. Statistical facts should be placed in relation to each other
Data become more meaningful when related observations can be compared.
For example, monthly sales figures can be compared to study whether sales are increasing, decreasing, or remaining stable.
In Short
According to Secrist's classical view, statistical data should generally be:
Aggregate + Numerical + Systematically collected + Purposeful + Reasonably accurate + Related
These points are particularly useful when preparing a traditional examination answer.
3. Definitions Given by A. L. Bowley
A. L. Bowley gave three well-known definitions of statistics, which focus on counting, averages, and the measurement of social phenomena:
1. Science of Counting:
Statistics may be called the science of counting.
This definition emphasizes counting or enumeration. That is, this definition is too narrow because it covers only one aspect of the science, namely, the collection of data.
Counting is certainly an important part of statistical work, but statistics involves much more than counting.
2. Science of Averages:
Statistics may rightly be called the science of averages.
This highlights how statistics summarizes large groups of data into representative central values.
This definition emphasizes averages.
The mean, median, and mode are important statistical measures. However, averages represent only one part of statistics.
Statistics also deals with:
- variation,
- probability,
- sampling,
- correlation,
- regression,
- estimation,
- hypothesis testing, and
- statistical inference.
Therefore, statistics cannot be understood only as the science of averages.
This definition is also not saisfactory because averages are only one of the devices used in statistical analysis. The other devices, like skewness, variation, correlation, etc. are not at all covered by this definition.
3. Science of Measurement of the Social Organism
Statistics is the science of the measurement of social organism, regarded as a whole in all its manifestations.
This broadens the view to examine social structures and collective human. This definition is also not satisfactory. Bowley himself recognized this when he remarked, “Statistics cannot be confined to any one science.”
This definition reflects the historical importance of statistics in studying social and economic phenomena.
However, the scope of modern statistics is much wider.
What can we learn from Bowley's definitions?
Bowley's different descriptions highlight different aspects:
Counting → Averages → Measurement
Each is useful, but none by itself represents the whole of modern statistics.
4. Definition of Statistics According to Croxton and Cowden
Croxton and Cowden gave a widely cited definition:
“Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.”
This definition is useful because it focuses on the major activities involved in statistical work.
Collection
First, relevant data are collected.
Presentation
The collected data can be presented using:
- tables,
- diagrams,
- graphs, and
- charts.
Analysis
Statistical methods are then used to study the data.
Examples include:
- Mean
- Median
- Mode
- Range
- Variance
- Standard deviation
- Correlation
- Regression
Interpretation
Finally, the results are interpreted so that meaningful conclusions can be drawn.
Some college-level texts expand this sequence by explicitly adding organization between collection and presentation:
Collection → Organization → Presentation → Analysis → Interpretation
This expanded sequence is useful for learning the complete process of a statistical investigation, although “organization” is not part of the Croxton and Cowden quotation itself.
Hence, Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of numerical data. Or, in general, a collection of quantitative data is referred to as statistics. In our daily lives, we see and use data.
In statistics, we learn how to organise and summarise data, and how to use formal methods to draw conclusions from “good” data after studying probability and probability distributions.
The Basic Statistical Process
A simple way to remember the basic process is:
Collection
↓
Organization
↓
Presentation
↓
Analysis
↓
Interpretation
Let us see this with a simple example.
Suppose a teacher wants to study the marks of 50 students.
Step 1: Collection
The teacher records the marks.
Step 2: Organization
The marks are arranged and classified.
Step 3: Presentation
A frequency table or graph is prepared.
Step 4: Analysis
The teacher calculates suitable measures such as the mean, median, or standard deviation.
Step 5: Interpretation
The teacher explains what the results indicate about the students' performance.
This is statistics in practice.
Is Every Number Statistical Data?
No. Every number is not necessarily statistical data.
Consider:
25
By itself, this number has no clear statistical meaning.
Now consider:
The ages of 25 students were recorded to study the age distribution of a class.
Here we have:
- observations,
- a defined group,
- a purpose,
- a variable (age), and
- data that can be analyzed.
This illustrates an important idea:
A number by itself is not enough to understand data. Context matters.
In modern statistics, data can also be categorical rather than numerical. For example, blood group, eye colour, or type of vehicle can be recorded as categorical data.
So, the classical statement that statistics deals with numerical facts should be understood in its historical context.
Statistics, Data, and a Statistic: Do Not Confuse Them
These three terms are related but different.
Data
Data are the recorded observations or values.
Example:
45, 52, 61, 72, 80
These are data values.
Statistics
Statistics is the discipline or body of methods used to collect, organize, analyze, and interpret data.
A Statistic
A statistic is a numerical measure calculated from sample data.
For example, if the mean mark of a sample of students is 68, then 68 is a statistic.
A statistic is often used to learn about a corresponding characteristic of a population, called a parameter.
This distinction is fundamental in modern statistics.
Is Statistics Only About Averages?
No.
This is one of the most common misconceptions among beginners.
Averages such as the mean, median, and mode are important, but they are only part of statistics.
Statistics also includes:
- Data collection
- Data presentation
- Measures of central tendency
- Measures of dispersion
- Probability
- Sampling
- Estimation
- Hypothesis testing
- Correlation
- Regression
- Experimental design
- Statistical modelling
- Data interpretation
For example, two classes may have the same average mark but very different amounts of variation. Therefore, looking only at the average may not tell the whole story.
Variation is a central feature of data, and statistical methods help us describe and understand it.
Statistics is More Than Calculation
A student may think that statistics means remembering formulas and putting numbers into them.
That is only one part of learning statistics.
A good statistical analysis also asks:
- Where did the data come from?
- How were the data collected?
- Was the sample appropriate?
- Is there any possible bias?
- How much variation is present?
- What does the result actually tell us?
- How uncertain is the conclusion?
- Can the result reasonably be generalized?
This is why statistical thinking is important.
Modern introductory statistics texts emphasize understanding data and statistical reasoning rather than treating calculations as the entire purpose of the subject.
Why is Statistics Important?
We live in a world full of data.
Governments, businesses, hospitals, schools, researchers, industries, and scientific organizations collect and analyze data to answer questions.
Statistics helps us:
- summarize large amounts of data,
- compare groups,
- describe variation,
- identify patterns,
- study relationships,
- estimate unknown quantities,
- evaluate evidence, and
- draw conclusions from sample data.
For example, a business may study sales data to understand customer demand. A researcher may use a sample to learn about a larger population. A teacher may analyze examination marks to understand students' performance.
A Simple Real-Life Example
Suppose the marks of ten students are:
45, 52, 60, 61, 65, 68, 72, 75, 80, 82
These numbers are the raw data.
We can now:
- arrange them,
- calculate the mean,
- find the median,
- calculate measures of variation,
- display them graphically, and
- interpret the overall performance.
If the same process is applied systematically to a larger study, statistics helps us move from raw observations to useful information.
Traditional and Modern Meaning of Statistics
It is useful to keep both viewpoints in mind.
Traditional viewpoint
Classical definitions often describe statistics as:
Aggregates of numerical facts collected systematically for a definite purpose and placed in relation to one another.
This viewpoint is particularly useful in traditional college and examination contexts.
Modern viewpoint
Modern statistics is better understood as:
A discipline that provides methods for learning from data, including data collection, description, analysis, inference, and interpretation while accounting for variability and uncertainty.
These two viewpoints are not contradictory.
The first focuses more on statistical data.
The second focuses more on statistical methods and statistical reasoning.
Exam-Friendly Definition of Statistics
If the question in an examination is:
“Define Statistics.”
You can write:
Statistics is the discipline concerned with the collection, organization, presentation, analysis, and interpretation of data for obtaining useful information and drawing appropriate conclusions.
For a traditional textbook-style answer, the Croxton and Cowden definition can also be written:
“Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.”
Very Short Answer
If only one or two lines are required:
Statistics is the study of data and the methods used to collect, organize, analyze, and interpret it.
Exam-Friendly Points: Characteristics of Statistics
For a longer examination answer, remember these classical characteristics:
- Statistics consists of an aggregate of facts.
- Statistical facts are generally numerically expressed in the classical sense.
- They are affected by multiple causes.
- They may be enumerated or estimated.
- They are collected with a reasonable standard of accuracy.
- They are collected in a systematic manner.
- They are collected for a predetermined purpose.
- They are placed in relation to each other.
Easy Memory Chain
Aggregate → Multiple causes → Numerical → Counted/Estimated → Accuracy → Systematic → Purpose → Relation
This is a useful memory aid for examinations.
Common Mistakes Students Make
Mistake 1: “Statistics means only averages.”
Incorrect.
Averages are only one part of statistics.
Mistake 2: “Every number is statistics.”
Incorrect.
A number without context may not constitute meaningful statistical information.
Mistake 3: “Statistics is only about calculation.”
Incorrect.
Collection, study design, analysis, interpretation, and communication are also important.
Mistake 4: Treating every classical definition as a complete modern definition
Classical definitions were developed in different historical contexts. They highlight particular aspects of statistics.
Mistake 5: Confusing “statistics” with “a statistic”
A statistic is a numerical measure calculated from sample data, whereas statistics is the broader discipline.
Frequently Asked Questions
What is statistics in simple words?
Statistics is a systematic way of working with data to understand what the data tell us.
What is the best definition of statistics?
There is no single historical definition that captures every aspect of the subject. A modern useful definition is:
Statistics is a discipline concerned with collecting, organizing, presenting, analyzing, and interpreting data to obtain information and draw appropriate conclusions while accounting for variability and uncertainty.
What is statistics according to Croxton and Cowden?
Croxton and Cowden defined statistics as the collection, presentation, analysis, and interpretation of numerical data.
What is statistics according to Horace Secrist?
Secrist described statistics as aggregates of facts affected by multiple causes, expressed numerically, collected systematically with reasonable accuracy for a predetermined purpose, and placed in relation to each other.
What did Bowley mean by “science of counting”?
Bowley's phrase emphasizes counting or enumeration as one aspect of statistical work. It is not a complete description of modern statistics.
Is statistics a branch of mathematics?
Statistics uses mathematics extensively, especially probability and mathematical statistics, but statistics is also a distinct discipline concerned with data, variability, inference, and statistical reasoning. Therefore, simply describing it as “a branch of mathematics” is an oversimplification for a modern introductory definition.
Is every numerical value statistical data?
No. Numerical values need context and a meaningful purpose before they can be understood as statistical information.
What is the difference between data and statistics?
Data are recorded observations or values. Statistics is the discipline and set of methods used to collect, organize, analyze, and interpret data. A statistic, in the technical sense, is a numerical measure calculated from sample data.
Final Takeaway
The meaning of statistics has changed and expanded over time.
Older definitions focused mainly on numerical facts, counting, averages, and the description of social conditions. Later definitions emphasized the processes of collection, presentation, analysis, and interpretation.
Modern statistics goes further. It is concerned with learning from data while paying attention to variation, sampling, uncertainty, study design, and the quality of evidence.
So, if you want one definition that is both simple and broadly useful, remember:
Statistics is the discipline of collecting, organizing, presenting, analyzing, and interpreting data to obtain useful information and draw appropriate conclusions in the presence of variability and uncertainty.
And for an examination, remember the simpler version:
Statistics is the study of data and the methods used to collect, organize, analyze, and interpret it.
apply.
Read More
- Objectives of Statistics
- Importance and Application of Statistics in Business and Management
- Characteristics of Statistics
- Nature of Statistics: Is Statistics a Science or an Art?
- Frequency Distribution in Statistics
- जीवन समंक क्या है? जीवन समंकों का अर्थ और परिभाषा (What is Vital statistics? Meaning and definition of Vital statistics in Hindi)
- Characteristics of Statistics in Hindi - सांख्यिकी की विशेषताएं
References and Further Reading
Modern Statistics
David S. Moore, George P. McCabe & Bruce A. Craig — Introduction to the Practice of Statistics, 10th ed., Macmillan Learning, 2021.
This is a major introductory statistics text that emphasizes statistical thinking, data analysis, interpretation, and understanding beyond calculations.
Barbara Illowsky & Susan Dean — Introductory Statistics, OpenStax.
Useful for fundamental concepts such as data, variables, sampling, variation, descriptive statistics, statistics, and statistical inference.
Indian College-Level Mathematical Statistics
S. C. Gupta & V. K. Kapoor — Fundamentals of Mathematical Statistics, Sultan Chand & Sons.
The text includes an introductory treatment of the meaning and scope of statistics, definitions of statistics, descriptive statistics, probability, distributions, correlation, regression, and statistical inference. It is a long-established Indian university-level reference.
Note on Classical Definitions
The definitions attributed to Webster, Horace Secrist, A. L. Bowley, and Croxton & Cowden are historical/classical definitions. Their purpose in this article is to explain how the concept of statistics has been described in traditional statistical literature. They should not be treated as interchangeable with a single modern definition of the discipline.
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