What do you call a branch of statistics that involves tabulating depicting and describing the collected data?

Statistics plays a main role in the field of research. It helps us in the collection, analysis and presentation of data. In this blog post we will try to learn about the two main branches of statistics that is descriptive and inferential statistics.

Statistics is concerned with developing and studying different methods for collecting, analyzing and presenting the empirical data.

The field of statistics is composed of two broad categories- Descriptive and inferential statistics. Both of them give us different insights about the data. One alone doesn’t not help us much to understand the complete picture of our data but using both of them together gives us a powerful tool for description and prediction.

Before starting with descriptive and inferential statistics let us get the basic idea of population and sample.

Population:

Population is the group that is targeted to collect the data from. Our data is the information collected from the population. Population is always defined first, before starting the data collection process for any statistical study. Population is not necessarily be people rather it could be batch of batteries, measurements of rainfall in an area or a group of people.

Sample:

It is the part of population which is selected randomly for the study. The sample should be selected such that it represents all the characteristics of the population. The process of selecting the subset from the population is called sampling and the subset selected is called the sample.

Descriptive Statistics

It describes the important characteristics/ properties of the data using the measures the central tendency like mean/ median/mode and the measures of dispersion like range, standard deviation, variance etc.

Data can be summarized and represented in an accurate way using charts, tables and graphs.

For example: We have marks of 1000 students and we may be interested in the overall performance of those students and the distribution as well as the spread of marks. Descriptive statistics provides us the tools to define our data in a most understandable and appropriate way.

Inferential Statistics

It is about using data from sample and then making inferences about the larger population from which the sample is drawn. The goal of the inferential statistics is to draw conclusions from a sample and generalize them to the population. It determines the probability of the characteristics of the sample using probability theory. The most common methodologies used are hypothesis tests, Analysis of variance etc.

For example: Suppose we are interested in the exam marks of all the students in India. But it is not feasible to measure the exam marks of all the students in India. So now we will measure the marks of a smaller sample of students, for example 1000 students. This sample will now represent the large population of Indian students. We would consider this sample for our statistical study for studying the population from which it’s deduced.

Some differences to remember!

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When analysing data, such as the marks achieved by 100 students for a piece of coursework, it is possible to use both descriptive and inferential statistics in your analysis of their marks. Typically, in most research conducted on groups of people, you will use both descriptive and inferential statistics to analyse your results and draw conclusions. So what are descriptive and inferential statistics? And what are their differences?

Descriptive Statistics

Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data. Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data.

Descriptive statistics are very important because if we simply presented our raw data it would be hard to visualize what the data was showing, especially if there was a lot of it. Descriptive statistics therefore enables us to present the data in a more meaningful way, which allows simpler interpretation of the data. For example, if we had the results of 100 pieces of students' coursework, we may be interested in the overall performance of those students. We would also be interested in the distribution or spread of the marks. Descriptive statistics allow us to do this. How to properly describe data through statistics and graphs is an important topic and discussed in other Laerd Statistics guides. Typically, there are two general types of statistic that are used to describe data:

• Measures of central tendency: these are ways of describing the central position of a frequency distribution for a group of data. In this case, the frequency distribution is simply the distribution and pattern of marks scored by the 100 students from the lowest to the highest. We can describe this central position using a number of statistics, including the mode, median, and mean. You can learn more in our guide: Measures of Central Tendency.
• Measures of spread: these are ways of summarizing a group of data by describing how spread out the scores are. For example, the mean score of our 100 students may be 65 out of 100. However, not all students will have scored 65 marks. Rather, their scores will be spread out. Some will be lower and others higher. Measures of spread help us to summarize how spread out these scores are. To describe this spread, a number of statistics are available to us, including the range, quartiles, absolute deviation, variance and standard deviation.

When we use descriptive statistics it is useful to summarize our group of data using a combination of tabulated description (i.e., tables), graphical description (i.e., graphs and charts) and statistical commentary (i.e., a discussion of the results).

Inferential Statistics

We have seen that descriptive statistics provide information about our immediate group of data. For example, we could calculate the mean and standard deviation of the exam marks for the 100 students and this could provide valuable information about this group of 100 students. Any group of data like this, which includes all the data you are interested in, is called a population. A population can be small or large, as long as it includes all the data you are interested in. For example, if you were only interested in the exam marks of 100 students, the 100 students would represent your population. Descriptive statistics are applied to populations, and the properties of populations, like the mean or standard deviation, are called parameters as they represent the whole population (i.e., everybody you are interested in).

Often, however, you do not have access to the whole population you are interested in investigating, but only a limited number of data instead. For example, you might be interested in the exam marks of all students in the UK. It is not feasible to measure all exam marks of all students in the whole of the UK so you have to measure a smaller sample of students (e.g., 100 students), which are used to represent the larger population of all UK students. Properties of samples, such as the mean or standard deviation, are not called parameters, but statistics. Inferential statistics are techniques that allow us to use these samples to make generalizations about the populations from which the samples were drawn. It is, therefore, important that the sample accurately represents the population. The process of achieving this is called sampling (sampling strategies are discussed in detail in the section, Sampling Strategy, on our sister site). Inferential statistics arise out of the fact that sampling naturally incurs sampling error and thus a sample is not expected to perfectly represent the population. The methods of inferential statistics are (1) the estimation of parameter(s) and (2) testing of statistical hypotheses.

We have provided some answers to common FAQs on the next page. Alternatively, why not now read our guide on Types of Variable?

Which branch of statistics involves tabulating depicting and describing the collected data?

What are the branches of statistics?

What is a branch of statistics that involves organizing and summarizing data?

What is the branch of statistics that involves drawing conclusions about a population based on information contained in a sample taken from that population?