Descriptive statistics

From Sustainability Methods
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Descriptive stats are what most people think stats are all about. Many people believe that the simple observation of more or less, or the mere calculation of an average value, is what statistics are all about. Of course, this is not the case - statistics is more than descriptive statistics, or whimsical bar plots or even pie charts. Still, knowing the basics is important, and most of you probably already calculated things like mean and median in school. So let us have another look to refresh your memory.

Basics of descriptive statistics

This graphic visualizes what mean, mode and median explain regarding a dataset.


The mean is the average of numbers you can simply calculate by adding up all the numbers and then divide them by how many numbers there are in total.


The median is the middle number in a sorted set of numbers. It can be substantially different from the mean value, for instance when you have large gaps or cover wide ranges within your data. Therefore, it is more robust against outliers.


The mode is the value that appears most often. It can be helpful in large datasets or when you have a lot of repetitions within the dataset.


The range is simply the difference between the lowest and the highest value and consequently it can also be calculated like this.

This graph shows how the standard deviation is spread from the mean.

Standard deviation

The standard deviation is calculated as the square root of variance by determining the variation between each data point relative to the mean. It is a measure of how spread out your numbers are. If the data points are further from the mean, there is a higher deviation within the data set. The higher the standard deviation, the more spread out the data.

R examples

Now, let us have a look at how to calculate these values in R.

#descriptive statistics using the Swiss dataset

#we are choosing the column fertility for this example
#let's begin with calculating the mean



#standard deviation

#summary - includes minimum, maximum, mean, median, 1st & 3rd Quartile

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