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, this measurable data is always collected in number form. 

Although there exist other data types which may appear in number form, numerical data differentiates itself with these 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. 


Types of Numerical Data 

There are two types of numerical data, namely; discrete data and continuous data. 

  • 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, they 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 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.

numerical-data-example

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

This 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. 


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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.

numerical-data-visualization 

Numerical Data Examples 

  • Census: The Federal Government periodically needs to conduct the census of a country to know the country's population and demographics of this population. A head-to-head count of the 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. 

  • Mark Grading: Numerical data is used when grading test scores. 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 may add up to your score. Therefore, the admission board may ask you to 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 admission score. 

  • 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.). It is sometimes called a continuous variable because it exhibits the characteristics 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. 

numerical-variable

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

This 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 & Interpretation 

Numerical data can be interpreted using two main statistical methods of analysis, namely; descriptive statistics and inferential statistics. 

Descriptive Statistics

This 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. 

numerical-analysis

Inferential Statistics

This 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.

  • Marketing & Advertising

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. 

Disadvantages of Numerical 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 it. 

With Formplus web-based data collection tool, you have access to features that will assist you in making strategic business decisions. This way, you can improve business sales, launch better products and serve customers better. 


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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.



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