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What is Numerical Data? [Examples,Variables &
Analysis]
By Formplus Blog | Last updated: Jun 25, 2020

When working with statistical data, researchers need to get acquainted
with the data types used—categorical and numerical data. The different
data types are used in separate cases and require different statistical and
visualisation techniques.

Therefore, researchers need to understand the different data types and
their analysis. This knowledge is what is used during the research process.

Numerical data as a case study is categorised into discrete and continuous
data where continuous data are further grouped into interval and ratio
data. These data types are significantly used for statistical analysis or
research purposes.

What is Numerical Data

Numerical data is a data type expressed in numbers, rather than natural
language description. Sometimes called quantitative data,numerical data is
always collected in number form. Numerical data differentiates itself with
other number form data types with its ability to carry out arithmetic
operations with these numbers.

For example, numerical data of the number of male students and female
students in a class may be taken, then added together to get the total
number of students in the class. This characteristic is one of the major ways
of identifying numerical data.

What are the Types of Numerical Data?

There are two types of numerical data, namely; discrete data-which
represent countable items and continuous data-which represent data
measurement. The continuous type of numerical data are further sub-
divided into interval and ratio data, which is known to be used for
measuring items.

• Discrete Data

Discrete Data is a type of numerical data which represents countable items.
They take on values that can be grouped into a list, where the list may
either be finite or infinite. Whether finite or infinite, discrete data take on
counting numbers like 1 to 10 or 1 to infinity, with these group of numbers
being countably finite and countably infinite respectively.

A more practical example of discrete data will be counting the cups of
water required to empty a bucket and counting the cups of water required
to empty an ocean—the former is finite countable while the latter is infinite
countable.

• Continuous Data:

This is a type of numerical data which represents measurements—their
values are described as intervals on a real number line, rather than take
counting numbers. For example, the Cumulative Grade Point Average
(CGPA) in a 5 point grading system defines first-class students as those
whose CGPA falls under 4.50 – 5.00, second class upper as 3.50 – 4.49,
second class lower as 2.50 – 3.49, third class as 1.5 – 2.49, pass as 1.00 – 1.49
and fail as 0.00 – 0.99..

A student may score a point 4.495, 2.125, 3.5 or any possible number from
0 to 5. In this case, the continuous data is regarded as being uncountably
finite.

Continuous data may be subdivided into two types, namely; Interval &
Ratio Data.

• Interval Data

This is a data type measured along a scale, in which each point is placed at
an equal distance from one another. Interval data takes numerical values
that can only take the addition and subtraction operations.

For example, the temperature of a body measured in degrees Celsius or
degrees Fahrenheit is regarded as interval data. This temperature does not
have a zero point.

• Ratio Data

Ratio data is a continuous data type similar to interval data, but has a zero
point. In other words, ratio data is an interval data with zero point. For
ratio data, the temperature may not only be measured in degrees Celsius
and degrees Fahrenheit, but also in Kelvin. The presence of zero-point
accommodates the measurement of 0 Kelvin.

General Characteristics/Features of Numerical Data

• Categories: There are two main categories of numerical data,
namely; discrete and continuous data. Continuous data is then further
broken down into interval and ratio data.

• Quantitativeness: Numerical data is sometimes called quantitative
data due to its quantitative nature. Unlike categorical data which
takes quantitative values with qualitative characteristics, numerical
data exhibits quantitative features. .

• Arithmetic Operation: One can perform arithmetic operations like
addition and subtraction on numerical data. True to its quantitative
character, almost all statistical analysis is applicable when analysing
numerical data.

• Estimation & Enumeration: Numerical data can both be estimated
an enumerated. In a case whereby the numerical data is precise, it
may be enumerated. However, if it is not precise, the data is
estimated. When computing the CGPA of a student, for instance, a
4.495623 CGPA is rounded up to 4.50.

• Interval Difference: The difference between each interval on a
numerical data scale are equal. For example, the difference between 5
minutes and 10 minutes on a wall clock is the same as the difference
between 10 and 15 minutes.

• Analysis: Numerical data is analysed using descriptive and
inferential statistical methods, depending on the aim of the research.
Some of the descriptive-analytical methods include; mean, median,
variance, etc. Inferential statistical methods like TURF analysis, trend

analysis, SWOT analysis etc. are also used for numerical data
analysis.

• Data Visualisation: Numerical data may be visualised in different
ways depending on the type of data being investigated. Some of the
data visualisation techniques adopted by numerical data include;
scatter plot, dot plot, stacked dot plot, histograms, etc.

What are the Examples of Numerical Data?

Numerical data examples which are usually expressed in numbers includes;
census data, temperature, age, mark grading, annual income, time, height,
IQ, CGPA etc. These numerical examples, either in countable numbers as in
discrete data or measurement form like continuous data call all be labelled
as an example of numerical data

• Census: The Federal Government periodically needs to conduct the
census of a country to know the country’s population and
country’s resident is done using numerical data.

Knowing the Census of a country assists the Government in making proper
economic decisions. It is an example of countably finite discrete data.

• Temperature: The temperature of a given body or place is measured
using numerical data. The body temperature of a body, given to be 37
degrees Celsius is an example of continuous data.

This data type also put into consideration the unit of measurement. Interval
data, for instance, can only measure in degrees Celsius and Fahrenheit,
while ratio data can also measure in Kelvin.

• Age: The age of an individual is counted using numerical data. It is
classified as quantitative because it can take up multiple numerical
values.

Although numbers are infinite in the real sense, the number of years people
spend in life is finite, making it a countably finite discrete data. For

example, a person who is 20 years old today may finish high school at 16, 4
years ago.

Most times, these marks are uncountably finite and fall under
continuous data.

When applying for admission in a school, for instance, your O level results
input your grades—A is 5 points, B is 4 points, C is 3 points, D is 2 points
and E is 1 point. All these points are added together to make your total

• Annual income: The annual income of an individual or household is
an example of numerical data, used by businesses to know the
purchasing power of their customers or each household in a
community. This knowledge influences the price of their
products. The annual income of an individual or household is a
countably finite discrete data.

• Time: The amount of time it took a runner to run a race, for instance,
is numerical data. It doesn’t matter whether it is being measured in
hours, seconds or minutes, it always takes a numeric value. Time is an
example of continuous data. It is regarded as interval data if
measured on a 12-hour clock.

• Height: A person’s height could be any value (within the range of
human heights), not just certain fixed heights. This height takes a
numeric value which varies in person and can increase as time goes
on.

The height of a person, measured in centimetres, metres, inches etc. is
continuous data.

• IQ Test Score: Most IQ tests rate a person’s IQ in terms of
percentage. The percentage of IQ is derived from the participant’s
score in various sub-tests.

This score is not only quantitative but also has quantitative properties. An
IQ test score is an example of uncountably finite categorical data.

• Weight: Weight is a variable element in humans. A person might
weigh 50kg while another might weigh 80kg. Unlike height that may
not decrease, weight may increase and decrease in a person.

The weight of a person measured in kg is a numerical data and may be an
indication of fat or slim which is a categorical variable.

• CGPA: This represents a student’s Grade Point Average in his/her
studies over a set period e.g. one semester. The mean of the GPA is
used to find the CGPA of a student over a longer period e.g. two
sessions. CGPA is an example of interval data.

• The number of children: The number of children in a community,
for instance, is a superset of the number of children in a home. In
other words, the number of children in each home is what adds up to
make the total number of children in counting.

This exhibits the characteristics of numerical data and is a countably finite
discrete data example.

• Number of students: Similarly, the number of students in a class is a
superset of the number of males and females in a class. That is, the
number of males and females is what adds up to make the total
number of students in a class.

The number of students in a class is also a countably finite discrete data
example.

• Results of rolling a dice: A die has six faces, with each face
representing one of the numbers from 1 to 6. When you roll a dice,
you get two numbers which may add up to one of 2, 3, 4, 5, 6, 7, 8, 9,
10, 11 and 12.

Therefore, the results of rolling dice is a countably finite discrete data
example.

• Length: Let us consider the length of a leaf for example, which is
similar to the height in human beings. A leaf’s length could be any
value, not just certain fixed length.

This height takes a numeric value which varies in plants and can increase
as the plant grows. The length of a leaf measured in centimetres is
continuous data.

Numerical Data Variables

A numerical variable is a data variable that takes on any value within a
finite or infinite interval (e.g. length, test scores, etc.). numerical variable
can also be called a continuous variable because it exhibits the features of
continuous data.Unlike discrete data, continuous data takes on both finite
and infinite values.

There are two types of numerical variables, namely; interval and ratio
variables.

An interval variable has values with interpretable differenced, but no true
zero. A good example is a temperature when measured in degrees Celsius
and degrees Fahrenheit.

Interval variable can be added and subtracted, but cannot be multiplied and
divided. Ratio variable, on the other hand, does all this.

Interval Variable

Interval variable is an extension of the ordinal variable, with a standardised
difference between variables in the interval scale. There are two
distributions on interval variables, namely; normal distribution and non-
normal distribution

Normal Distribution

A real-valued random variable is said to be normally distributed if its
distribution is unknown. We consider two main samples of normal
distribution and carry out different tests on them.

Matched Sample

Tests

• Paired t-test: This is used to compare two sample population
means.

• Repeated measures ANOVA: This compares means across three
or more variables, based on repeated observations.

Unmatched Sample

Tests

• Unpaired t-test: This is used to compare two sample population
means.

• ANOVA: This compares means across three or more variables,
based on a single observation.

Non-Normal Distribution

A real-valued random variable is said to be non-normally distributed if its
distribution is known. We consider two main samples of non-normal
distribution and carry out different tests on them

Matched Sample

Tests

• Wilcoxon rank-sum test: This is used to compare two groups of
matched samples.

• Friedman 2-way ANOVA: This is used to compare the difference
in means across 3 or more groups.

Unmatched Sample

Tests

• Wilcoxon rank-sum test: This test is used when the requirements
for the t-test of two unmatched samples are not satisfied.

• Kruskal-Wallis test: This is used to investigate whether three or
more groups of unmatched samples originate from the same
distribution.

Ratio Variable

Ratio variable is an extension of interval variable, with values with a true
zero and can be added, subtracted, multiplied or divided. The tests carried
out on these variables are similar to those of interval variables.

Numerical Data Analysis

Numerical data analysis can be interpreted using two main statistical
methods of analysis, namely; descriptive statistics and inferential
statistics. Numerical analysis in inferential statistics can be interpreted
with swot, trend and conjoint analysis while descriptive statistics makes
use of measures of central tendency,

Descriptive Statistics

Descriptive statistics is used to describe a sample population using data
sets collected from that population. Descriptive statistical methods used in
analysing numerical data are; mean, median, mode, variance, standard
deviation, etc.

Inferential Statistics

Inferential is used to make predictions or inference on a large population-
based on the data collected from a sample population. Below are some of
the methods used for analysing numerical data.

• Trend analysis: Trend analysis is an interval data analysis technique,
used to draw trends and insights by capturing survey data over a
certain period.

• SWOT analysis: SWOT is an acronym for Strengths, Weaknesses,
Opportunities and Threats. Strengths and Weaknesses are for
internal analysis, while Opportunities and Threats are for external
analysis of an organisation.

• Conjoint analysis: This is a market research analysis technique that
investigates how people make choices.

• TURF analysis: This is an acronym for Total Unduplicated Reach and
Frequency analysis, and is used to assess the market potential for a
combination of products or services.

Uses of Numerical Data

• Population Prediction

Using Trend analysis, researchers gather the data of the birth rate in a
country for a certain period and use it to predict future population.
Predicting a country’s population has a lot of economic importance.

Before engaging in any marketing or advertising campaign, companies need
to first analyse some internal and external factors that may affect the
campaign. In most cases, they use a SWOT analysis.

• Research

Numerical data is very popular among researchers due to its compatibility
with most statistical techniques. It helps ease the research process.

• Product Development

During the product development stage, product researchers use TURF
analysis to investigate whether a new product or service will be well-
received in the target market or not.

• Education

Interval data is used in the education sector to compute the grading system.
When calculating the Cumulative Grade Point Average of a student, the
examiner uses an interval data of the student’s scores in the various
courses offered.

• Medicine

Doctors use the thermometer to measure a patient’s body
temperature as part of a medical check-up. In most cases, body
temperature is measured in Celsius, therefore passing as interval
data.

• Preset answers that do not reflect how people feel about a subject.
• “Standard” questions from researchers may lead to structural bias.
• Results are limited.

What is the best tool to collect Numerical Data?

Numerical data is one of the most useful data types in statistical analysis.
Formplus provides its users with a repository of great features to go with
features that will assist you in making strategic business decisions. This
way, you can improve business sales, launch better products and serve
customers better.

Conclusion

Numerical data research techniques employ inquiry strategies such as
experiments and surveys. The findings may be predictive, explanatory, and
confirming.

It involves the collection of data which is then subjected to statistical
treatment to support or refute a hypothesis. Thus, numerical data
collection techniques are used to gather data from different reliable
sources, which deal with numbers, statistics, charts, graphs, tables, etc.

Reference

Formplus Blog, (2020), What is Numerical Data? [Examples,Variables & Analysis], Retrieved August 22,
2020 from https://www.formpl.us/blog/numerical-data

• What is Numerical Data
• What are the Types of Numerical Data?
• General Characteristics/Features of Numerical Data
• What are the Examples of Numerical Data?
• Numerical Data Variables
• Interval Variable
• Normal Distribution
• Tests
• Unmatched Sample
• Tests
• Non-Normal Distribution
• Matched Sample
• Tests
• Unmatched Sample
• Tests
• Ratio Variable
• Numerical Data Analysis
• Descriptive Statistics
• Inferential Statistics
• Uses of Numerical Data