Descriptive Statistics Examples: From Zero to Hero!

Descriptive statistics examples are the basic skill that should be mastered as a researcher. As basic statistics, it can never be separated in data analysis.

Descriptive statistics have an important role in data exploration so as to provide meaning that is more useful for data users.

Almost in every study, descriptive statistics are always displayed directly or indirectly. After the data is explained descriptively, the researcher usually submits the inference analysis so that both provide explanations that are able to answer the research objectives.

Descriptive statistics is one of the most powerful tools to present information.

What is descriptive statistics?

Descriptive statistics is a type of data analysis to help, display, or summarize the data in a meaningful way to make the data insightful for the user.

The main goal of descriptive is to describe the characteristics of the data.

Descriptive statistics are used to manage data so that it has deeper information. The task of a researcher is to make that confidential information appear and be known to as many people as possible.

The purposes of descriptive statistics are:

1. Collecting

With descriptive statistics, the data collection process will run neater, easier, and faster.

2. Organizing

Descriptive statistics make data management more neat, easy to process, and easy to understand.

3. Summarizing

Descriptive statistics produce important information related to data characteristics that can be used in analyzing an event or phenomenon.

4. Presenting

Descriptive statistics make data appear in a format that is easier to understand and interesting. You can use media such as tables, graphics, infographics, etc. so that the data you use can be understood quickly by the reader.

purposes-of-descriptive-statistics

There are two common types of descriptive statistics:

1. Numerical analysis

Numerical analysis is descriptive statistics that aim to make data simpler and more meaningful in the form of numerical measures.

Numeric representation is a descriptive statistic that aims to make data simpler in the form of numerical measurements. In this case, there are various measurements such as central tendency, dispersion, and asymmetry.

2. Data Visualization

Data visualization aims at descriptive statistics that aim to present data in visual or graphical form so that it is more interesting and easier to understand.

I will show an interesting descriptive statistics examples at the end of the article. Keep reading!

types-of-descriptive-statistics

The measure of descriptive statistics

There are 3 types of measurement in descriptive statistics.

1. The measure of central tendency

The measure of central tendency is the most common method used in descriptive analysis. This method focuses on describing the condition of the data at the central point.

In general, we can see how the condition of the data by looking at where the data center is located. Normally, the data center itself will be at the middle value, although this is not always the case.

To prove this mathematically, measurements that are often used are the mean, median, and mode. We discuss one by one.

Mean is the average of the data sets we have. The formula is very simple. You only need to add up the value of all the data you have and divide it by the amount of data.

Median is the middle value of a data. If we have a set of data, we can sort the data from the smallest to the largest value. If we have an odd amount of data, then the middle value of that data will immediately be the median.

But if we have even data, we need to find the average value of the middle value of the data.

The mode is the value that most often appears in a group of data. We just need to see which values ​​appear most often in the group. If the number of frequencies for each data is the same, there is no mode value.

Central tendency is the most popular measurement of descriptive statistics examples.

2. Measure of dispersion

The diversity measure is a measure to present how the data is distributed. A measure of diversity shows how the condition of data is spread across the group of data that we have. This allows us to analyze how far the data is scattered from the size of its concentration.

If the data distribution is low, this shows that the data is spread not far from its center. If the distribution is far away, it shows that the data is far from its center.

To illustrate this, you can use the following measurement.

1. Range

Range is the difference between the largest value and the smallest value we have. Range is the simplest and easiest thing to understand in terms of distribution. Range shows how far the distribution without considering the shape or the form of the distribution.

2. Quartiles Range

Quartiles range or quartile range is a measure of spread that divides data into 4 parts. As the name implies, the quartile divides the data into 25 percent in each part.

There are 3 types of quartile values that we need to know:

• Q1 or lower quartile containing 25 percent of the data with the lowest value

• Q2 or the middle quartile, which divides the data into 2 equal parts: the smallest 50 percent and the largest 50 percent. Q2 also has the same value as the median.

• Q3 or upper quartile which contains 25 percent of the data with the highest value.

3. Percentile

Percentile is a size of distribution that divides data into 100 equal parts.

4. Decile

Decile is a spread size that divides data into 10 equal parts.

5. Variance

Variance is a measure of how far it spreads from the average value. The smaller the value of the variance, the closer the data distribution is to the average. The greater the variance value, the greater the distribution of data against the average value.

6. Standard deviation

Standard deviation is another measure of the distribution of data against the average. If you use variance, the value you get is very huge. Sometimes, this value is not able to describe how the actual data distribution to the average.

To get a value that is more easily interpreted, the standard deviation is a more appropriate measure. The standard deviation produces a smaller value and is able to explain how the data is spread to the averag6. Skewness

3. Measure of asymmetry

1. Skewness is a measure that shows how lean the data is to the average. Skewness can also be said as a measure of the asymmetry of data.

Sk = 0 means that the shape of the DF curve is considered normal.

Sk < 0 means that the DF curve tends to be left-skewed.

Sk > 0 | meaning that the DF tends to be right-skewed.

2. Kurtosis (alpha 4)

Kurtosis is a measure that shows how the data is tangled in its distribution. Kurtosis is commonly referred to as the degree of stroke. Kurtosis is calculated by the formula of the fourth moment of the average.

• kurtosis value = 3, meaning that the data has a normal distribution

• kurtosis value > 3, meaning that the data has a leptokurtic distribution (more pointed)

• kurtosis value < 3 means that the data has a platycurtic distribution (more flat).

Data visualization

Data visualization aims to convey and present data so that information is more easily understood by data users. With visualization, data can be presented in a form that is more interesting and has a more meaningful meaning.

The most basic thing in data visualization that is closest to our lives in the table. Using tables, we can summarize information in the form of rows and columns so as to make the presentation of data simpler.

It’s just that the table feels less informative when used in very large sizes. We will have difficulty obtaining important points from the data we have just by displaying the data in tabular form.

Therefore, we need other media that can describe data so as to produce more meaningful information.

One of the most frequently used media in data visualization is the chart. The chart is a method used to present information to make it look more attractive, informative, and easier to understand according to the characteristics of the data.

  • If you want to compare data, you can use bar charts or line charts. You can easily compare the differences between the data between times or between categories.
  • If you want to see the composition of the data, you can use a pie chart. With a pie chart, you can see what proportion of each group of data you have.
  • If you want to see the characteristics, you can use a stacked bar chart or spider chart. With this graph, you can see the characteristics between time or between groups of data so that it is more easily understood.
  • If you want to see the relationship between data, you can use scatterplots. This is commonly used as an initial detection in the use of correlation analysis and regression analysis.

Of course, there is an unlimited way to present your data in an informative method. You could use an infographic, video graphic, combining bar and line chart, heat map, bubble map, pie chart, etc. to make an outstanding chart.

Unleash your creativity so the user will get a better knowledge of your research.

If you are looking at how to create a better data visualization, I will recommend you this three software:

1. Data wrapper

2. Tableau

3. Power BI

Trust me, these three or even just using one software will significantly improve your descriptive statistics.

Descriptive statistics examples for research

Descriptive statistics can be used for qualitative and quantitative research.

In quantitative research, you may use both numerical analysis and data visualization to present your data in a better form to the reader.

You can also summarize all of the descriptive statistics measurements to provide deep and information.

But, what about descriptive statistics for qualitative research? Could we present it to the reader?

Okay, we have two types of descriptive statistics: numerical analysis and data visualization.

In the case of using data visualization, there will no problem with it. You could make a table, chart, graph, etc which contain qualitative information in it.

This is an example of how to make a table by using qualitative research.

descriptive-statistics-for-qualitative-research

See? It becomes easier and informative for the reader by the methods above.

But, what about numerical analysis, could we present it?

If you want to present numerical analysis for qualitative research which uses a categorical variable, you have to process the data into numerical form so it has the specific value that you want to show.

The data process should be coded specific, detail, and comparable so you can (at least) make a simple classification by using the numerical table and then present it in numerical analysis.

This is the requirement that you have to fulfill to present the numerical analysis.

Descriptive statistics example

Now, I will try to make short descriptive statistics examples by COVID-19 data from New Zealand. We are going to make a simple descriptive statistics using SPSS and visualization with Power BI.

This is the daily data from December, 13rd 2019 to June, 5th 2020. The total is 156 data.

Note: I am not going to explore the detailed steps. We only talk about the output here and a simple way to make the data meaningful. If you are interested to know the details, take the full steps on how to use descriptive statistics with SPSS.

descriptive-statistics-output-spss

Based on the output above, we could explain.

1. The average test per day for COVID-19 is 1857. The maximum capability of testing is 7812 and the minimum is 0. The daily test has a large variation in the last 5 months (156 days).

2. The average of the new case is 0.14. It means almost 0 cases per day for the last 5 months. The maximum case is 4 and the minimum case is 0.

3. The average of death cases is 7.40. It means, in the last 5 months, 7 people death almost every day because of COVID-19. The maximum death a day is 95 and the minimum is 0.

data-visualization-with-power-BI
Source: Our world in data

Using another interesting data, see the following picture!

Pictures speak a thousand words, is not it?

Most cases happen in mid-march to mid-may. It’s quite interesting how the government handles the pandemic for two months and make the curve flatten.

The new death case is also small. It means the recovery rate for the COVID-19 patients it quite a height. We could also assume that the health system in New Zealand is very responsive and fantastic.

I am not epidemiologic so It’s hard for me to give a deeper explanation of the descriptive statistics examples above. You can explore it based on the theory.

Data visualization is an interesting thing to explore more descriptive statistics examples. It is very powerful and insightful, is not it?

How to create descriptive statistics report

After the previous descriptive statistics examples, we also need to learn how to write a descriptive analysis report properly. How to explain it to the reader so they will understand it and have a meaningful insight.

Usually, I categorize my report like this.

1. Specify the measure of central tendency.

Mean, median, and modus are the top three that always we have to put in the report. You may write it for each variable so you will see the difference between them.

2. Specify the measure of dispersion

Variance and standard deviation are the most important part that you have to put on the report.

3. Analyze the value of data

The value that you have to put is minimum, maximum, range, and outlier. We could detect that your data is normally distributed or not by using this.

4. Analyze the shape distribution

Use kurtosis and skewness to measure the shape of data distribution. It helps to decide how the data distributed from the mean. Also, show the histogram!

5. Visualize the data

Data is visualization is super important. Choose the right one.

6. Spot the interesting data

When analyzing, you will find interesting data such as extremely high, or extremely low, or increasing significantly, and so on. Spot it, and make a great explanation of it.

7. Make a scientific explanation.

After deciding the numbers above, making the data visualization, now you can make a proper explanation. Not only a common explanation but a powerful description. Do not forget to add a scientific explanation.

Summary

There are two types of descriptive statistics:

1. Numerical analysis

2. Data Visualization

Three common measurements of statistics:

1. The measure of central tendency

2. Measure of dispersion

3. Measure of asymmetry

To make a powerful descriptive statistics report, follow these steps:

1. Specify the measure of central tendency.

2. Specify the measure of dispersion

3. Analyze the value of data

5. Visualize the data

6. Spot the interesting data

7. Make a scientific explanation.

By doing this, you have done great descriptive statistics example and reach your main goal to describe your data characteristics.

If you are interested to produce a complex and powerful analysis, I will recommend you to see these inferential statistics examples!

Leave your comment below! Cheers!

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