Master Descriptive Statistics: Key Concepts & Practical Guide

Descriptive statistics is one of the types of statistics, which is the type that focuses on collecting and transforming data into numbers, in order to be statistically analyzed to achieve reliable scientific results that a researcher can rely on in his scientific research, so descriptive statistics is the branch related to methods of collecting, tabulating, organizing, presenting and summarizing information, and data and describing data distribution, using frequency tables or graphs, as well as finding some numerical or descriptive measures that describe data distribution.

In the current article, we will together learn about the definition of descriptive statistics, its importance, and its most important uses, while clarifying the most important differences between descriptive and inferential statistics, including some examples of descriptive statistics in scientific research.

Definition of Descriptive Statistics:

Descriptive statistics is ‘a branch of statistics that deals with methods of collecting data and summarizing it in the form of numbers, organizing and arranging and presenting this data in a simple way through tables or graphs, with the calculation of some statistical measures in order to give an initial description of the phenomenon under study’.

Descriptive statistics includes a set of statistical principles that help in describing human and social phenomena, that is, descriptive measures, which help the researcher to put the data in a form that is easy to understand, interpret, and know the degree of its availability in the original society.

Importance of Descriptive Statistics:

The importance of descriptive statistics as one of the branches of statistics emerged due to modern developments, which contributed to achieving many achievements in many fields and specializations, as the importance of descriptive statistics is manifested in:

1. Simplifying large and complex data, by presenting it in a table or graph and expressing and describing it with simplified numbers that are easy to understand.
2. Putting facts in a general and clear picture by using numbers that clarify the facts more than an ordinary sentence would.
3. Comparing different variables and finding the relationship between them, and representing this relationship with mathematical models.
4. Enabling researchers in different sciences to make appropriate decisions with a high degree of accuracy based on the available data.
5. Descriptive statistics helps in the planning process because it is used in the process of predicting future data.
6. Statistical methods help in the classification process, such as classifying students according to their ages and averages.

Uses of Descriptive Statistics:

Descriptive statistics is used in a large number of different scientific specializations, and the most important of these uses are:

1. Descriptive statistics is used in most economic studies that aim to predict and plan, whether at the level of institutions or at the level of the national economy.
2. Descriptive statistics is widely used in the field of business and accounting studies, such as analyzing financial statements, searching for indicators and accounting standards, and predicting commercial or industrial profits.
3. Descriptive statistics is used in demographic studies to express many demographic indicators such as births, deaths, migration and so on.
4. Statistical measures in their various uses are the foundation of social research as they are used in various studies such as population events, measuring age, marriage periods, and others.

Don’t miss an article aboutTheories in Scientific Research.

Principles of Descriptive Statistics:

The principles of descriptive statistics and its possibility of use in research and studies are manifested in the most commonly used statistical measures, which are divided into:

1. Measures of central tendency.
2. Measures of dispersion.

First: Measures of Central Tendency (averages):

Measures of central tendency are “summarizing data in a numerical form by calculating some statistical measures known as measures of central tendency or averages, which describe to us how the phenomenon under study is distributed in the sample in an accurate and concise manner suitable for comparing two or more phenomena” and the most important types of them are:

1- Arithmetic Mean:

It is one of the most important and most famous measures of central tendency and the most common and used, it is the result of dividing a set of data values by their number,

2- Median:

It is one of the best measures of central tendency and the most used in describing data of groups or frequency distributions that contain outliers or extreme values, as it is not affected at all by the type and nature of the values, and it is defined as the value that divides the statistical series into two equal parts after arranging the values in ascending or descending order.

3- Mode:

The mode represents the value that corresponds to the absolute maximum frequency or the relative maximum frequency in the statistical series, and therefore it is the most widespread and common value of the statistical variable or the dominant value, or more precisely it is “the point that indicates the most frequent value in the distribution”.

Second: Measures of Dispersion:

Measures of dispersion are “measures that clarify the extent of the spread of the values of the statistical series around a central value, i.e., their deviation or the closeness of some to each other, and this is called dispersion, and they are considered alternative measures to measures of central tendency, when it is impossible for us to describe or compare a result due to the equality of the calculated averages”, and the most important types of them are:

1- Range:

It is called the range or the general range, and it is one of the simplest measures of dispersion in concept and application, it expresses the extent of variation of the statistical phenomenon, and it is defined as “the difference between the largest and smallest value in the given data”,

2-Variance:

Variance is “the average of squared deviations from the mean, that is, it is the square of the standard deviation”. Variance in this sense is considered one of the most important measures of dispersion due to its direct reliance on the standard deviation, and it is on the other hand one of the averages because it is essentially an average of squared deviations. Therefore, it is suitable for measuring collective differences between different types of frequency distributions, such as calculating the differences between the levels of achievement of male and female students with respect to any of the academic subjects.

2- Standard Deviation:

The standard deviation is “the positive square root of the variance, and it is one of the most important and most used measures of dispersion in descriptive statistical studies”, and it is one of the most accurate measures of dispersion, although it is affected by extreme values as is the case with the arithmetic mean.

The standard deviation is used to measure the correlation between random variables, and in time series to measure the correlation relationship between the studied phenomenon and time.

Learn about the most importantmethods of data collection in scientific research

The Difference Between Descriptive and Inferential Statistics:

The difference between descriptive and inferential statistics can be clarified through the following:

1. Descriptive Statistics:It is concerned with collecting, classifying, summarizing, and displaying data in tables or through charts.
2. Inferential Statistics:It deals with statistical methods used in data analysis and interpretation of results.
3. Descriptive Statistics:It aims to classify data and provide a simple description of measures and charts.
4. Inferential Statistics:It aims to draw conclusions about the source from which the data was collected by relying on probability theory.
5. Descriptive Statistics:Summarizing a large number of statistical data into a limited number of numbers is called statistical measures. Or in an easy-to-read statistical table.
6. Inferential Statistics:It moves from the part to the whole according to specific statistical methods that fall under applied statistics.

Example of Descriptive Statistics:

An example of descriptive statistics can be clarified through the various statistical measures mentioned above:

Example of the Arithmetic Mean:

For example, if the ages of 5 employees in a certain institution are (30, 50, 45, 38, 28), then the arithmetic mean of this data is:

Sum of employees’ ages / their number, which is: 30+50+45+38+28 / 5 = (Arithmetic mean: 38.2).

Example of the Median:

For example, we calculate the median for the following values (4, 2, 3, 10, 8, 6, 11) arranged in ascending order: (2, 3, 4, 6, 8, 10, 11), the median is the number (6).

Example of the Mode:

Calculate the mode for each of the following groups:

1- The first group: (1, 10, 20, 30, 40, 50, 70, 90).

The mode in the first group: There is no mode because no values are repeated more than others.

2- The second group: (2, 10, 20, 15, 18, 20, 20, 17).

The mode in the second group: There is one mode, which is (20) as it is the most repeated value in the second group.

The third group: (3, 19, 19, 18, 19, 20, 18, 15).

In the third group: there is a mode which is the value (19) because it is the most repeated value compared to others? There is also another mode which is the value (18) which also repeated in the same group, and if there are two modes it is called (bimodal distribution).

Example of Range:

It is calculated through the following equation:

Range = Largest value – Smallest value.

As an applied example, calculate the general range of the following values: (5, 8, 12, 10, 15, 6)

The solution: the largest value is 15 and the smallest value is 5, so the solution is 15-5 = (the range is 10).

Related Articles:

1. The inductive approach in scientific research
2. The quantitative approach in scientific research
3. How to prepare a research methodology effectively

Conclusion of the Article:

In this article, we have illustratively presented descriptive statistics and its most important uses in scientific research, in addition to clarifying its importance in research with addressing the most important statistical measures and the most common ones in descriptive statistics, furthermore, we provided a brief comparison between descriptive statistics and inferential statistics with presenting some practical examples through mathematical problems about descriptive statistics in research, we hope that this article has met your satisfaction and attention, with our best wishes to all researchers and postgraduate students at the master’s and PhD stages for success and integrity.

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