When you are gathering information whether in a classroom exam, a customer survey or a science experiment, you usually have very large quantities of digits. With these raw numbers, you really cannot tell much until you are able to summarize them. And this is where descriptive statistics find a place. It enables the reduction of large-sized data to make the most out of it and have a smaller, simpler and easier to digest result.
This blog will define descriptive statistics, explain the types, graph types, look at examples, and interpret results. We are also going to point out the importance of descriptive statistics in research, how one uses descriptive statistics in SPSS, and the strengths and weaknesses of descriptive statistics.
What is Descriptive Statistics?
The definition of descriptive statistics is easy; it is the subdivision of statistics which consists of summarizing, tabulating, and presenting information in a manner that makes sense and is intelligible. Rather than considering each and every data point, descriptive statistics aim at building up a summary of the data.
To take an example, suppose that you are a teacher who has 200 students in your class. On an exam, you are left with a long list of scores. When you receive a question on how your students performed, you cannot hand over the whole list- it will become overwhelming. Rather than that, you can simply say the average score was 75, the top score was 95, and the bottom one was 30. This brief overview describes all the information about the statistics without demonstrating each and every figure. It is the work of descriptive statistics.
Types of Descriptive Statistics
Descriptive statistics are of two categories: measures of central tendency and measures of variability. The two help in giving the full picture of your data.
1: Measures of Central Tendency
The Measures of Central Tendency concentrate on the centermost or medium worth in your information. These include:
- Mean (the arithmetic average of the data).
- Median (the middle number when the data is arranged in order).
- Mode (the most frequently occurring value).
For example, in the data set [40, 50, 50, 60, 70], the mean is 54, the median is 50, and the mode is 50. . These are measurements that would provide an indication of where the majority of the values are.
2: Measures of Variability
Measures of Variability (dispersion) tell about the extent to which the data is spread apart. These include:
- Range (the difference between the highest and lowest values).
- Variance (the average squared deviation from the mean).
- Standard Deviation (how far data points tend to be from the average).
Consider the two classrooms in which the mean score on an exam is 75. Everyone in one of the classes was getting between 70 and 80. In the latter, the lowest scorer was 30 and the highest 95. Although the averages are equal, the second class contains a more dispersion and this is reflected in its standard deviation.
Descriptive Statistics Graph Types
Numbers are occasionally difficult to read unto themselves. It is due to this reason that graphs and charts are considered in descriptive statistics. They give a graphical overview of the data that is very easy to assimilate.
The most common descriptive statistics graph types include:
- Histograms: Illustrate the occurrence of values in a data set, e.g. grades among students.
- Bar Charts: Useful when you want to make comparisons such as sales of various products.
- Pie Charts: Using pie charts to show proportions, the market share in the case of companies.
- Box Plots: These represent the medians, quartile lines, and outliers and this can be used to identify aberrant data points.
To take an example, 200 student scores could be displayed in a table, but a histogram can indicate whether most of the students got above average scores, below average scores, or just the average. Data is brought to life through visuals.
Descriptive Statistics Examples
To get a better understanding of how descriptive statistics are used in practice, we will examine some examples of descriptive statistics:
- Education: A teacher reports about the performance of his or her class based on the average mark, the best mark and the worst.
- Healthcare: A physician process is going through data collected on patients by determining the mean blood pressure of a population and the number of patients whose blood pressure is within the normal range.
- Business: Business shows the average monthly sales, the most sales of a year past and the variability of the regions.
- Sports: To report on the performance of a player, analysts the total number of points he/she scored per match or goals per match.
These are illustrations of how descriptive statistics make data redundant into information that can lead to making certain decisions.
Descriptive Statistics Interpretation
Interpretation of the numbers is more important than the number itself providing the value of descriptive statistics. Interpretation of descriptive statistics involves giving a meaningful explanation of what those figures and graphs imply about the data.
Suppose the average salary in one firm is $60000, but the standard deviation is very big, then what it implies is that despite the average salary being $60000, there are those employees that will have very low salaries or there are those who may have very high salaries. This could be used to expose unequal pay between the various individuals in the company
In the same way exam results can be presented in a box plot such that the majority got between 60 and 80 however there are outliers at the very bottom. This allows the teacher to know that most students are performing in a good manner but there is a need to support some other students. Descriptive statistics on its own is nothing more than numbers. Through it the data turns into a story.
Role of Descriptive Statistics in Research
Descriptive statistics in research are very important. It serves as the baseline in which other statistical methods are developed on Descriptive statistics provide an understanding of the data before researchers make any inference about the data using advanced models and hypothesis testing.
Descriptive statistics are useful in research to assist in:
- Summarize the data that has been obtained.
- Identify trends and patterns and anomalies.
- Elaborate results in an easy manner for the audience.
- Start with a foundation that leads to the moving into inferential statistics.
In a psychology example, they can describe the age, gender and test score of the participants using descriptive statistics before letting the relationships between the variables be tested. Without the former step, more analysis would be out of context.
Descriptive Statistics Examples in SPSS
One of the most commonly used tools in data analysis is known as the SPSS (Statistical Package for the Social Sciences). It is particularly very easy in use to the researchers and students. The SPSS examples of descriptive statistics are as follows:
- The creation of the mean, medium, and mode of the survey reactions with a couple of clicks.
- To determine the spread out of data values, computing standard deviation and variance.
- Producing graphs such as histograms or bar graphs automatically to depict the data.
To illustrate, you may have a survey of 500 respondents in terms of their income level and using SPSS, one can easily tell the average income, the lowest, the highest and the distribution of income among the respondents. Rather than making manual calculations, the software does it at real-time.
Descriptive Statistics in Quantitative Research
Quantitative studies deal with numerical information and the descriptive statistics in quantitative research take the leading position in representing it. It is used by researchers to:
- The demographic background of the participants (i.e., average age, the percentage of males and females).
- Summarise answers to questionnaires and experiments.
- Compare groups of averages
In another survey on customer satisfaction, descriptive statistics can tell how 80 percent of customers described the service as good or excellent. The brief illustration of such research findings can make them more understandable and effective.
Advantages and Disadvantages of Descriptive Statistics
As all tools, descriptive statistics have advantages and disadvantages.
Advantages
- Easy to understand: Averages and charts are simple to comprehend even by an ordinary person.
- Quick summaries: Bulky data is summarized in easy-to-understand patterns.
- Broad applications: It is used in education, business, healthcare, and scientific research.
- Foundation for further analysis: Forms a preliminary platform before the more sophisticated statistics analysis.
Disadvantages
- Limited scope: It is not able to predict the future and can only describe existing data.
- No causal explanations: It does not tell you why things are like that, only tells what they are like.
- Risk of oversimplification: The simplification of data into a few numbers can run the risk of losing important facts.
As an example, it is useful to mention that the average score on an exam in a certain class is 75, but it does not actually explain why some could perform so much better, almost twice as good, as others.
Final Thoughts
Descriptive statistics are far more than average. It is central to transforming meaningless numbers into something that makes a lot of sense in terms of their condensations, arrangement, and picture representation. Descriptive statistics provides an overview of data because it is the way to analyze classroom test results, sales performance, or survey data, in terms of a larger picture. By studying what descriptive statistics are, finding out more about the various forms of graphs, and putting tools such as SPSS into use, you can develop insightful information out of statistics to make better decisions. The importance of descriptive statistics in the research cannot in any way be understated since without the former they cannot be analyzed further statistically.
