Data in Statistics: Types, Raw Data, Grouped Data, Discrete and Continuous Data
Data is the foundation of statistics. Statistical methods begin with collecting observations or measurements and then organising, presenting, analysing, and interpreting them.
Whether we are studying students' marks, population figures, temperatures, income, production, or survey responses, we first need data.
In this article, we will learn the meaning of data in statistics, its major types, and the difference between raw data, qualitative data, quantitative data, discrete data, continuous data, grouped data, and ungrouped data.
What is Data in Statistics? Data, Information and Statistical Data in Statistics
In statistics, data are observations or measurements recorded for the purpose of study, analysis, or decision-making.
Data: Factual information, such as measurements or statistics, that is used as a basis for argument, discussion, calculation, etc., is called data.
An observation may describe a person, object, event, or characteristic.
Data are facts, observations, measurements, or other recorded values collected for reference, analysis, or decision-making. So, basically, data is a collection of information, observations, or measurements. Data may be numerical or non-numerical.
In other words, any piece of information that may be expressed as a value or a numerical number is called data. For example, the number of vehicles that passed through a highway in an hour is data, and the marks you received on your exam is also data.
For example, suppose the marks obtained by five students are:
42, 55, 68, 71, 84
These five values are observations. Together, they form a data set.
Other examples of data include:
- heights of students
- weights of patients
- number of books in a library
- daily temperature
- monthly income
- number of customers visiting a shop
- blood groups of students
- responses to a survey
- production of a factory
Important Point
Data are not necessarily numbers.
For example:
- Height = 170 cm → numerical data
- Temperature = 28.5°C → numerical data
- Blood group = A+ → categorical data
- Eye colour = Brown → categorical data
Therefore, it is incorrect to say that all data must be numerical.
Types of Data in Statistics
A useful basic classification is:
Data
→ Qualitative / Categorical Data
→ Quantitative Data
Quantitative data can be further classified as:
→ Discrete Data
→ Continuous Data
Let us understand each type.
1. Qualitative Data
Qualitative data describe categories or qualities rather than numerical amounts.
They are also commonly called categorical data.
Examples include:
- Blood group: A, B, AB, O
- Eye colour: Brown, Blue, Green
- Type of vehicle: Car, Bus, Truck
- Marital status: Single, Married, etc.
- Type of school: Public, Private
- Grade: A, B, C, D
For example, if the blood groups of five students are:
A+, B+, O+, O+, A+
these observations are categorical data.
The values identify categories rather than measuring a numerical amount.
Exam Point
Qualitative data describe categories or attributes.
2. Quantitative Data
Quantitative data are numerical observations that represent amounts or quantities.
They are obtained through counting or measurement.
Examples:
- Age = 21 years
- Height = 168.5 cm
- Weight = 62 kg
- Number of students = 50
- Monthly income = ₹40,000
- Temperature = 32.4°C
Quantitative data are commonly classified into discrete and continuous data.
3. What is Discrete Data?
Discrete data are quantitative data that take distinct, countable values.
They commonly arise from counting.
Discrete data is the data that is recorded in whole numbers, such as the number of members in a family or the number of animals in a zoo. Discrete data cannot be in fractions or decimals.
Examples:
- Number of students in a class
- Number of books on a shelf
- Number of children in a family
- Number of cars in a parking area
- Number of calls received in one hour
- Number of defective products
For example:
A classroom may contain:
40, 41, 42, 43, ... students
The number of students is a count. We do not normally have 40.5 students.
Therefore, the number of students is a discrete variable.
Easy Rule
If you count it, it is generally discrete.
4. What is Continuous Data?
Continuous data are quantitative data obtained by measurement and capable of taking values throughout an interval.
Continuous data does not have to be expressed in whole numbers; it can also be expressed in decimals. For example, your percentage of marks, the temperature in a city for a week, etc.
Examples include:
- Height
- Weight
- Temperature
- Time
- Distance
- Length
- Volume
For example, the height of a person may be recorded as:
170 cm
or, with greater measurement precision:
170.5 cm
or:
170.52 cm
The underlying variable, height, is treated as continuous because it is measured on a continuum.
Easy Rule
If you measure it, it is generally continuous.
Important Note
Do not define continuous data simply as “data containing decimal values.”
The important idea is not the decimal point itself. The important question is whether the variable is measured and can take values throughout an interval.
Discrete Data vs Continuous Data
| Basis | Discrete Data | Continuous Data |
|---|---|---|
| Basic idea | Distinct, countable values | Measured values that can vary over an interval |
| Common source | Counting | Measurement |
| Examples | Number of students, books, cars | Height, weight, temperature, time |
| Values | Separate possible values | Potentially any value within a relevant interval |
| Easy clue | Count | Measure |
Example
Number of students = 45
→ Discrete
Height = 165.7 cm
→ Continuous
Number of books = 125
→ Discrete
Weight = 62.35 kg
→ Continuous
A Common Question: Can Discrete Data Have Decimal Values?
The discrete data is based on distinct, countable values, not simply on whether a number contains a decimal point.
For example, a count such as the number of objects normally takes whole-number values.
Therefore, for introductory statistics:
Countable values → discrete
Measured values on a continuum → continuous
The nature of the variable is more important than the way a particular number happens to be written.
What is Raw Data?
Raw data are observations in the original form in which they were collected, before they have been processed, classified, or analysed.
The term "raw data" means an initial collection of information, which hasn't been properly organised yet. We will get raw data, after the very first step of data collection.
Ex 1: If we ask a group of five students about their exam scores, and their responses are 8, 9, 7, 10, and 6. This collection of information is called raw data.
Ex 2: Suppose a teacher asks five students for their examination marks and records:
72, 58, 81, 64, 75
These observations, as originally collected, are raw data.
The data can later be:
- arranged in order,
- classified,
- presented in a table,
- converted into a frequency distribution,
- represented by a graph,
- or analysed using statistical measures.
Example
Raw data:
72, 58, 81, 64, 75
Arranged data:
58, 64, 72, 75, 81
The observations are the same, but their presentation has changed.
Exam Definition
Raw data are observations in their original collected form before statistical processing or analysis.
What is Ungrouped Data?
Ungrouped data are data presented as individual observations rather than being combined into class intervals.
Ungrouped data are data that have not been arranged in a systematic fashion. Ungrouped data is data that has not been put into a group or category after collection.
Data is classified into numbers or attributes (characteristics), so data that is not placed in either category is called ungrouped data. When collecting data, priority is given to ungrouped data, as it contains the information in its original form.
For example:
12, 15, 18, 12, 20, 17, 15, 19
Here, the individual observations are shown directly.
For a relatively small data set, this form can be useful because it preserves the individual values.
Ungrouped Frequency Data
Ungrouped data can also be presented as a frequency table when the distinct values are listed separately.
Suppose the data are:
2, 3, 2, 4, 3, 2, 5
They can be presented as:
| Value | Frequency |
|---|---|
| 2 | 3 |
| 3 | 2 |
| 4 | 1 |
| 5 | 1 |
This is an ungrouped frequency distribution because each distinct value is listed separately rather than being combined into class intervals.
What is Grouped Data?
Grouped data are data that have been classified into groups or class intervals and presented with their frequencies.
Data in the form of a frequency distribution is called grouped data. Data that has been classified into groups after it has been collected is called grouped data.
The raw data is organised into many groups and a table is made. The table's main purpose is to show the data points that appear in each group.
For example, when a test is completed, the results are the data in this situation, and there are many methods for grouping this data.
Suppose the marks of a large number of students are between 0 and 100.
Instead of listing every individual mark, we can use class intervals:
| Marks | Frequency |
|---|---|
| 0–10 | 3 |
| 10–20 | 7 |
| 20–30 | 12 |
| 30–40 | 15 |
| 40–50 | 9 |
The observations have been combined into intervals.
This is called a grouped frequency distribution.
Why Do We Group Data?
Suppose a researcher has thousands of observations.
Writing every observation separately may make the data difficult to understand.
Grouping can:
- reduce the size of the presentation,
- make patterns easier to see,
- make frequency distributions easier to construct,
- help with graphical presentation,
- and make large data sets easier to summarise.
However, grouping has a limitation.
When individual observations are combined into class intervals, some information about the exact individual values is no longer directly visible.
Therefore:
Grouping makes large data sets easier to summarise, but it can reduce detail about individual observations.
Grouped Data vs Ungrouped Data
| Feature | Ungrouped Data | Grouped Data |
|---|---|---|
| Arrangement | Individual values are shown | Values are combined into groups/classes |
| Class intervals | Usually absent | Usually present for continuous or large data |
| Detail | More individual detail is retained | Some individual detail is lost |
| Suitable for | Smaller or less complex data sets | Large data sets |
| Example | 12, 15, 18, 20, 22 | 10–20, 20–30, 30–40 |
| Frequency | May be given for individual values | Usually given for each class |
Raw Data vs Ungrouped Data
The terms raw data and ungrouped data are closely related, but they do not necessarily describe exactly the same idea.
Raw Data
Raw describes the stage or form of the data after collection.
It means the observations are in their original collected form before processing or analysis.
Ungrouped Data
Ungrouped describes the way the observations are arranged.
It means the observations have not been combined into class intervals or groups.
Therefore:
Raw = original collected form
Ungrouped = not combined into groups or class intervals
In introductory statistics, the two terms are sometimes used interchangeably, especially when a list of original observations is being discussed. However, keeping the distinction above is useful for precise statistical writing.
What is Statistical Data?
The phrase statistical data refers to data consisting of observations or measurements collected and used for a statistical investigation.
Government agencies often publish data, such as unemployment rates or educational literacy rates. These kinds of data are called "statistical data". Hence, statistical data is a sequence (collection) of observations made on a group of items that are part of a population sample.
For example, a researcher studying the heights of university students may collect the heights of 500 students.
Those observations form a statistical data set for the study.
Statistical data can relate to:
- individuals,
- households,
- businesses,
- schools,
- countries,
- physical measurements,
- economic variables,
- scientific experiments,
- surveys,
- and many other subjects.
Statistical data may be qualitative or quantitative, and quantitative data may be discrete or continuous.
Data, Information, and Statistics
These three terms are related, but they should not be treated as synonyms.
Data
Data are recorded observations, measurements, or facts.
Example:
45, 52, 61, 70, 72
These values are data.
Information
In a general data-processing context, information is data that have been organised, processed, summarised, or interpreted so that they provide meaningful context.
For example:
The five students have an average mark of 60.
This statement is a meaningful summary obtained from the original observations.
Statistics
The word statistics has more than one closely related use.
◾Statistics as a subject
Statistics is the discipline concerned with collecting, organising, presenting, analysing, and interpreting data.
◾A statistic as a numerical measure
A statistic can also mean a numerical quantity calculated from sample data.
For example, suppose a sample contains:
10, 15, 20, 25, 30
Its sample mean is:
\[ \bar{x}=\frac{10+15+20+25+30}{5}=20 \]
Here, 20 is a statistic because it is calculated from sample observations.
Difference between Data and Information:
The main differences between data and information are as follows:
- Data is a collection of unorganised and unprocessed facts. Information is made up of processed, organised data that is presented in a meaningful context.
- Data is a single unit that consists of raw materials that have no special meaning. Information is a collection of data that has a logical meaning when taken together.
- Data is not dependent on information, but the information is dependent on data.
- Bits and bytes are the units of measurement for computer data. Time, quantity, and other meaningful units are used to measure information.
For decision-making, raw data is insufficient. For example, the test score of a student is called data.
For decision-making, information is sufficient. For example, the average marks of a class are called information produced from the given data.
Data vs Information
| Data | Information |
|---|---|
| Recorded observations or facts | Data presented or processed to provide meaning or context |
| May consist of individual observations | Often involves organisation, summarisation, or interpretation |
| Used as input for analysis | Helps communicate what the data show |
| Example: 40, 50, 60, 70, 80 | Example: The mean mark is 60 |
Important Note
The distinction between data and information is broader than statistical terminology and can vary somewhat across disciplines. In statistics, the more important formal concepts are observations, variables, data sets, populations, samples, statistical summaries, and inference.
Difference between Data and Statistics
The words "data" and "statistics" are frequently interchanged, but between the two there is an important distinction in scholarly research.
- Data are individual pieces of factual information that are recorded and used for analysis. It is the raw information that creates statistics.
- The results of the data analysis – their interpretation and presentation – are statistics.
- In other words, some calculation has taken place that gives some understanding of the meaning of the data. Statistics are frequently displayed in the form of a table, chart, or graph, but this is not required.
Data vs Statistics
| Data | Statistics |
|---|---|
| Data are observations or measurements. | Statistics is the discipline that deals with data. |
| Data are collected from individuals, objects, events, or processes. | Statistical methods organise, analyse, and interpret data. |
| Example: 10, 15, 20, 25, 30 | Example: Mean = 20 |
| Individual observations may be numerous. | Statistical summaries can reduce many observations to useful numerical measures. |
Exam-Friendly Definition
Data are observations or measurements collected for a statistical study, whereas statistics is the discipline concerned with the collection, organisation, presentation, analysis, and interpretation of data. A statistic is also a numerical measure calculated from sample data.
A Complete Classification of Basic Data Types
The following structure is useful for beginners:
DATA
◾Qualitative / Categorical Data
Examples:
- Blood group
- Eye colour
- Type of vehicle
- Grade
◾Quantitative Data
▪️Discrete Data
Usually obtained by counting.
Examples:
- Number of students
- Number of books
- Number of calls
▪️Continuous Data
Usually obtained by measurement.
Examples:
- Height
- Weight
- Temperature
- Time
- Distance
This classification is particularly useful because it connects the nature of the variable with the statistical methods used later.
Real-Life Examples
Example 1: College Students
Suppose a college records:
- Age
- Height
- Blood group
- Number of siblings
- Course enrolled
Classification:
| Variable | Type |
|---|---|
| Age | Quantitative |
| Height | Quantitative continuous |
| Blood group | Qualitative/categorical |
| Number of siblings | Quantitative discrete |
| Course enrolled | Qualitative/categorical |
Example 2: Hospital Data
A hospital records:
- Patient age
- Body temperature
- Blood group
- Number of previous visits
- Diagnosis category
Possible classification:
| Variable | Type |
|---|---|
| Age | Quantitative |
| Body temperature | Quantitative continuous |
| Blood group | Qualitative/categorical |
| Number of previous visits | Quantitative discrete |
| Diagnosis category | Qualitative/categorical |
Example 3: Manufacturing
A factory records:
- Number of products manufactured
- Weight of each product
- Product type
- Number of defective products
- Production time
Possible classification:
| Variable | Type |
|---|---|
| Number manufactured | Quantitative discrete |
| Product weight | Quantitative continuous |
| Product type | Qualitative/categorical |
| Number defective | Quantitative discrete |
| Production time | Quantitative continuous |
Common Mistakes About Data
Mistake 1: All data are numbers
Wrong.
Categorical observations such as blood group or eye colour are also data.
Mistake 2: Every decimal value is continuous data
Wrong.
The underlying variable and how it is obtained matter more than the presence of a decimal point.
Mistake 3: Discrete data simply means “whole numbers”
This is a useful beginner shortcut, but it is not the best complete definition.
A better definition is:
Discrete data consist of distinct, countable possible values.
Mistake 4: Continuous data means “data with decimals”
Not exactly.
Continuous variables are generally measured and can take values throughout an interval.
Mistake 5: Raw data and ungrouped data always mean exactly the same thing
They are often used interchangeably in introductory contexts, but technically they emphasise different properties.
- Raw → original collected form
- Ungrouped → not combined into groups or class intervals
Mistake 6: Statistics means only calculations
Statistics is much broader than calculating an average.
It includes the systematic process of:
collecting → organising → presenting → analysing → interpreting data
Short Definitions for Quick Revision
Data
Data are recorded observations or measurements collected for a particular purpose.
Qualitative Data
Qualitative data describe categories or attributes rather than numerical amounts.
Quantitative Data
Quantitative data represent numerical amounts and are obtained through counting or measurement.
Raw Data
Raw data are observations in their original collected form before processing or analysis.
Discrete Data
Discrete data are quantitative data that take distinct, countable values.
Continuous Data
Continuous data are quantitative data obtained by measurement and capable of taking values throughout an interval.
Statistical Data
Statistical data are observations or measurements collected for a statistical investigation or analysis.
Ungrouped Data
Ungrouped data are observations presented individually rather than combined into class intervals.
Grouped Data
Grouped data are observations classified into groups or class intervals and summarised by their frequencies.
Information
Information is data that have been organised, processed, summarised, or interpreted to provide meaningful context.
Statistics
Statistics is the discipline concerned with collecting, organising, presenting, analysing, and interpreting data.
Frequently Asked Questions
What is data in statistics?
Data are recorded observations or measurements collected for a particular purpose and used in statistical analysis.
What are the main types of data?
At a basic level, data can be classified as qualitative (categorical) or quantitative. Quantitative data are commonly classified as discrete or continuous.
What is raw data?
Raw data are observations in their original collected form before they are processed, classified, or analysed.
What is discrete data?
Discrete data are quantitative data that take distinct, countable values, such as the number of students in a class.
What is continuous data?
Continuous data are quantitative data obtained by measurement and capable of taking values throughout an interval, such as height or temperature.
What is grouped data?
Grouped data are observations classified into groups or class intervals and presented with their frequencies.
What is ungrouped data?
Ungrouped data are observations presented individually rather than being combined into class intervals.
What is the difference between discrete and continuous data?
Discrete data are generally obtained by counting and have distinct possible values. Continuous data are generally obtained by measurement and can take values throughout an interval.
Are raw data and ungrouped data the same?
Not necessarily. Raw data refer to the original collected form, while ungrouped data refer to observations that have not been combined into groups or class intervals. The terms are sometimes used interchangeably in introductory statistics.
What is the difference between data and information?
Data are recorded observations or facts. Information is data that have been organised, processed, summarised, or interpreted to provide useful meaning or context.
What is the difference between data and statistics?
Data are observations or measurements, whereas statistics is the discipline that provides methods for collecting, organising, presenting, analysing, and interpreting data. A statistic can also mean a numerical measure calculated from sample data.
Key Takeaways
Remember these simple ideas:
Data → observations or measurements
Qualitative → categories or attributes
Quantitative → numerical amounts
Discrete → distinct, countable values
Continuous → measured values that can vary over an interval
Raw → original collected form
Ungrouped → individual values, not class intervals
Grouped → values combined into groups or class intervals
Statistics → methods and discipline for working with data
Data are the foundation of statistical work. They may describe categories or numerical quantities, and quantitative data may be discrete or continuous.
After data are collected, they can be organised and presented in different ways. Individual observations may be presented as ungrouped data, while large sets of observations can be classified into groups or class intervals to form grouped frequency distributions.
Understanding these basic ideas is essential before studying frequency distributions, measures of central tendency, measures of dispersion, probability, correlation, regression, sampling, and statistical inference.
The most useful habit for a statistics student is not to memorise isolated definitions. Instead, ask:
What is being observed?
Is it a category or a numerical quantity?
If numerical, is it counted or measured?
How are the observations being organised?
These questions make the classification of data much easier to understand and apply.
Read More
- Objectives of Statistics
- What is Statistics? Definition, Meaning & Examples
- Characteristics of Statistics
- Nature of Statistics: Is Statistics a Science or an Art?
- Importance and Application of Statistics in Business and Management
- 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
The conceptual framework and terminology in this article are based on standard university-level statistics textbooks:
-
Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers & Keying E. Ye, Probability & Statistics for Engineers & Scientists, 9th Edition, Pearson.
-
Jay L. Devore, Probability and Statistics for Engineering and the Sciences, 9th Edition, Cengage.
-
David S. Moore, George P. McCabe & Bruce A. Craig, Introduction to the Practice of Statistics, 9th Edition, Macmillan Learning.
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