What is Descriptive Statistics? Definition, Types Explained

Descriptive statistics are organized and summarized characteristics of the data set. The collection of observations from the entire population or sample is known as a data set. The first step after collecting data is to describe responses of the characteristics such as the average of one variable or relation between two variables. For example, finding a connection between age and creativity gives us statistical analysis. 

The next step is to find inferential statistics, which indicates whether your data refutes or confirms the hypothesis. It also helps us to decide whether a generalized population influences it. These days, researchers give a lot of importance to data science and big data, making this data processed with utmost scrutiny. This is where descriptive statistics kicks in.

One of the essential steps for analyzing descriptive statistics is that it gives descriptions, constructively shows data points, and provides insightful data information. It further gives you a conclusion of data distribution, helps you detect outliers, and enables you to identify similarities among variables.

Types of Descriptive Statistics

• Frequency Distribution

A frequency distribution shows the count or frequency of the different outcomes in a sample or data set. It is used for both qualitative and quantitative data and is typically presented in a graph or table format. Each entry in the graph or table is accompanied by the frequency or count of the values’ occurrences in a range, interval, or specific group. 

To make it clear, it is a summary or presentation of grouped data categorized based on exclusive classes. It also presents the number of occurrences in each respective category. Thus, it indicates a more organized and structured way to present raw data. 

Some of the examples of frequency distribution data are graphs or charts used in frequency presentation. In addition, pie charts, bar charts, line charts, and histograms are also an indicator of frequency distribution.

• Central Tendency

The central tendency generally refers to descriptive data set summary, using a single value that reflects the center of data distribution. Thus, measures of central tendency are popularly known as measures of central location. The three core aspects of central tendency are:

• Mean

Mean is considered to be the most popular central tendency. It is an average or most common value of the data set. To define mean, it is the simplest mathematical average of two or more numbers. Mean is given by the set of numbers in data, which can be computed in more than one way. There are two types of mean – arithmetic mean and geometric mean.  

For example, to find the mean of the following set of data; 2,3,4,5,6. Then, the mean of this data is four by simply adding the data set and dividing it by the number of values in the data set.

• Median 

The Median is the middle score of any data set in ascending or descending order. Thus, the list of numbers is more descriptive in the data set than average. 

For example, in the case of an odd data set that is {3, 13, 2, 34, 11, 26,47}, you need first to arrange the data {2,3,11,13,26,34,47}, here the Median is 13 because there are equal numbers on either side of the series. On the other hand, In case of even data set that is {3, 13, 2, 34, 11, 17, 27, 47}, you need to first arrange the data in an order {2,3,11,13,17,26,34,47}, here the Median would be the sum of two digits which are in the middle of the series divided by 2. Therefore, the Median would be 13+17/2, which is equal to 15.

• Mode

Mode refers to the score value which is most frequent in the data. The data set may have one mode, more than one mode, and no mode at all. 

For example, the data set having numbers {3,5,6,6,6,8,9}, the mode would be 6, and in case the data set has no same numbers, then that data is considered to have no mode.

• Variability 

Variability is a measure of summary statistics that reflects the degree of dispersion in a sample. It also measures the variability that determines how far apart the data points appear from the centre.

Spread, dispersion, and variability refer to the width and range of distribution values in a data. Standard deviation, variance, and range are used to depict different aspects and components of the spread. 

The range in the set of values depicts the degree of dispersion or an ideal distance between the lowest and highest values within a data. Standard deviation is used to establish the average variance in a set of data. It also provides an insight into the difference or distance between values in the data set. It depicts the mean value of the data as well. Finally, it reflects the degree of the spread. 

Importance of Descriptive Statistics

• Vigilant data

The data collected for descriptive statistics must possess a high degree of objectivity. Therefore, one needs to be extra vigilant because if the statistics show different characteristics of the data extracted and they don’t match the trends, it will be of no use.

• Broader Approach

Descriptive statistics is measured to be more vast than the quantitative method. It aims to provide a broader picture of the phenomenon or event. This can use a single number of variables or any number of variables to do research.

• Natural Relation

This statistical data is considered a better method for collecting information because it is natural and exhibits the world as it exists. It researches the real-life behavior of the data to ensure the accuracy of extracted trends. 

•  Flexible

Descriptive statistics gives the study a new way to learn things. For instance, researchers can use a case study that is both correlation and qualitative to describe the phenomena of descriptive statistics. One can use case studies to describe events, people, and institutions. This will enable researchers to understand data patterns and behavior. 

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• Identify variables and hypotheses