Have you been assigned the task to conduct a descriptive analysis or a research paper on descriptive statistics? If so, then you have nothing to worry, for we have come up with all the basic concepts that you need to get clear with for your paper. Let us get down with the fundamentals of descriptive statistics then, shall we? We will start with the definition of descriptive statistics.
DESCRIPTIVE STATISTICS: DEFINITION
A descriptive statistic is a summary
statistic that summarises the features of a group of data. Descriptive
statistics means the process of analysing those statistics collectively.
Unlike inferential statistics, descriptive stats are not developed on the
fundamentals of probability theory. This is precisely why descriptive
statistics is often termed as non-parametric statistics.
WHAT IS DESCRIPTIVE STATISTICS?
In short, descriptive statistics helps in describing
and understanding the features of a specific set of data by giving summaries
about the samples and the measures of the data. The reason why descriptive
statistics is called non-parametric is that it does not allow us to conclude
beyond the information given. It is just a simple way to describe and present
the data in a consolidated form.
Descriptive statistics are very important to define descriptive research and consolidate it. Since raw data is tough to visualise, it would be challenging to comprehend the message that the data was reflecting, especially if there were many data sets with different parameters. Descriptive statistics help us present data in a more meaningful way, thus allowing simpler interpretation of collected information. For example, if we had the grades of 100 students on particular or various assignments, it would be difficult to judge the overall performance of the students at a glance. Moreover, with many subjects interspersed, it would be tough to analyse the distribution of the marks. But with descriptive statistics, we can describe data from one standpoint and derive an average value.
The most common types of descriptive statistics are
mean, median, and mode and they are used at all levels of math and statistics.
There are other types of descriptive statistics too. We will discuss them later
in the blog.
THE MAIN PURPOSE OF DESCRIPTIVE STATISTICS
Descriptive statistics is used to repurpose complex
quantitative information due to the vastness of a data set and present it in
bite-sized explanations. GPA is a classic example of the usage of descriptive
statistics in the daily walks of life. Students usually take a wide range of
exams and classes throughout the year. That would mean many grades and average
percentages. Instead of putting all the grades scored, GPA takes data points
together to provide a general understanding of the overall academic performance
of a student.
Descriptive statistics are used even when a
descriptive analysis draws its key conclusions through inferential statistics.
Wondering how? Let us explain with an example. For instance, a survey was
conducted on the citizens of the USA to find out how many people thought the
government should provide medical insurance coverage to every citizen. In such
a case, the subject, i.e. human beings, will be divided into important
subgroups with separate demographics with clinical characteristics. Some of the
possible sub-groups would be average age, sex, height, weight, medical history,
etc. so how do you arrive at a single answer when you have so many dynamic
subjects? With the descriptive coefficients of descriptive statistics, it would
become easier to summarise the given data set and create a middle-ground from
all the different sectors.
TYPES OF DESCRIPTIVE STATISTICS
Descriptive statistics can be classified into the measures of central tendency and the measures of variability. Measures of central tendency include mean, median, and mode. And measures of variability encompass standard deviation, variance, calculation of minimum and maximum variables, and kurtosis and skewness.
In total, there are four types of descriptive statistics, and they are:
- Measures of Frequency – This includes three kinds – Count, Percent and Frequency, and shows how often something has occurred. You can use this if you want to show how many times a subject has given a response. For example, you can calculate how many times a student has scored an A in the same subject
- Measures of Central Tendency – Such measures are used to describe the central position of a frequency distribution for a data set. This includes Mean, Median, and Mode and is used to locate the distribution of data by various points. You can use this to show how the average response or the most common answer. For example, you can show the frequency distribution and pattern of marks scored by the 100 pupils in an ascending or descending order.
- Measures of Dispersion or Variation – This type revolves around the range, variance, and the standard deviation. It identifies the spread of data by stating the intervals. Range indicates the high and low points. Variance and Standard Deviation shows the difference between the observed score and mean. This type is used to showcase how widely the data is spread out. For example, the mean score of 100 students is 75 out of 100. However, not all students may have scored 75 marks. Typically, their scores will be spread out. Some might be lower than 75 and others might score more than 75. You can summarise how dispersed these scores are by using the measures of spread or dispersion.
- Measures of Position – Including percentile ranks and quartile ranks, this kind of descriptive statistic highlights how one response is related to one another provided that they are standardized. This type is used when the need for data comparison emerges. For example, if you want to find out the range, then descriptive statistics of position can be used on the 100 students.
DIFFERENCE BETWEEN DESCRIPTIVE AND INFERENTIAL STATISTICS
Here are some of the points that you can discuss while
bringing out the contrast between descriptive and inferential stats.
- Level of
certainly – Under descriptive statistics, the data set that you
want to describe is selected, and then every subject in that group is measured.
There is no measurement error in the statistical summary that describes the
group and the answer is entirely certain. However, in inferential statistics,
you define the population and then create a sampling plan as a representative
sampling process. As the name suggests, the statistical results are inferred
and therefore may be uncertain.
- Level of
difficulty – Descriptive study, by definition, is easier to
perform as there are definite formulas and techniques. However, in the case of
inferential stats, you need to collect evidence to show the existence of a
relationship between variables. Since there are no definite ways to arrive at a
conclusion, your answer may differ with someone else’s.
- Level of
generalisation – Although descriptive statistics are used to
ascertain coefficients such as the spread and range of the data, it cannot be
used to make generalisations. Despite inferential statistics using mean and
standard deviation, the process starts with a sample and then generalises to a
Now that you have a clear idea of the fundamental
concepts of descriptive statistics, you can start working on your descriptive
research or analysis paper. You can also use our samples to master the
techniques to measure the range, dispersion or deviation.
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