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.
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.
There are two types of numerical data, namely; discrete data and continuous 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.
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.
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.
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.
Knowing the Census of a country assists the Government in making proper economic decisions. It is an example of countably finite discrete 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.
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.
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.
The height of a person, measured in centimetres, metres, inches etc. is continuous data.
This score is not only quantitative but also has quantitative properties. An IQ test score is an example of uncountably finite categorical data.
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.
This exhibits the characteristics of numerical data and is a countably finite discrete data example.
The number of students in a class is also a countably finite discrete data example.
Therefore, the results of rolling dice is a countably finite discrete data example.
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.
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.
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.
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
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.
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
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 can be interpreted using two main statistical methods of analysis, namely; descriptive statistics and inferential 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.
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.
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.
Numerical data is very popular among researchers due to its compatibility with most statistical techniques. It helps ease the research process.
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.
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.
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.
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.
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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