Examples of Descriptive Statistics

examples of descriptive statisticsIn statistics, data is everything. When you collect your data, you can make a conclusion based on how you use it. Calculating things, such as the range, median, and mode of your set of data is all a part of descriptive statistics. Descriptive statistics can be difficult to deal with when you’re dealing with a large set of data, but the amount of work done for each equation is actually pretty simple.

Learning statistics can be a great asset for you in the work world. In fact, people who master statistics can get high level jobs, such as an actuary. If you want to start learning more about statistics and what it can be applied for, check out the Udemy course Introductory Statistics Part 1: Descriptive Statistics. The following examples will help you understand what descriptive statistics is and how to utilize it to draw conclusions.

What is Descriptive Statistics? 

When put in its simplest terms, descriptive statistics is pretty easy to understand. Descriptive statistics helps you describe and summarize the data that you have set out before you. You can, make conclusions with that data. When you make these conclusions, they are called parameters. This is a lot different than conclusions made with inferential statistics, which are called statistics.

Descriptive statistics involves all of the data from a given set, which is also known as a population. With this form of statistics, you don’t make any conclusions beyond what you’re given in the set of data. For example, if you have a data set that involves 20 students in class, you can find the average of that data set for those 20 students, but you can’t find what the possible average is for all the students in the school using just that data.

Within descriptive statistics there are two key types, and in those types you will find the different forms of measurements that you will perform with the data that you have.

Descriptive statistics has a lot of variations, and it’s all used to help make sense of raw data. Without descriptive statistics the data that we have would be hard to summarize, especially when it is on the large side. Imagine finding the mean or the average of hundreds of thousands of numbers for statistical analysis.

There are simpler ways to do descriptive statistics, such as with computer software. The Udemy course Descriptive Statistics in SPSS is a great tool to help you with descriptive statistics for incredibly large amounts.

Exploring the Two Types of Descriptive Statistics  

The first type of descriptive statistics that we will discuss is the measure of central tendency. These are the different ways in which we describe a group based on its central frequency. There are several ways in which we describe this central position, such as with the median, mean and mode.

When performing statistics, you will find yourself discovering the median, mean, and mode for various sets of data. You’re probably already familiar with discovering the mean of a number, which is also commonly known as the average, but the median and mode are important as well.

Examples of Finding the Median, Mean, and Mode

It’s easy to perform the arithmetic for the mean, median, and mode. In fact, for many of these forms of descriptive statistics, you don’t have to do any arithmetic at all.

For example, finding the median is simply discovering what number falls in the middle of a set. So let’s look at a set of data for 5 numbers. The following numbers would be 27, 54, 13, 81, and 6.

Now you would think that the median would be 13, since it sits in the middle of the data set, but this isn’t the case. An important thing to remember about the median is that it can only be found once you’ve rearranged the data in the order from largest to smallest.

When you rearrange this data set, the order of the numbers becomes 6, 13, 27, 54, and 81. Now the median number is 27 and not 13.

Another important thing to remember about the median is when you have an even number in your data set. When the set is even, you take the two numbers that sit in the middle, add them together and then divide them by two. Your result is the answer.

Let’s add onto the data set from above to find the mode. 6, 6, 13, 27, 53, 53, 53, 81, and 93 will be the numbers for this data set. Notice that some of the numbers repeat. When you’re finding the mode for a set of numbers, the mode is the number in the data set that appears the most times. In this instance, 53 is the mode since it appears 3 times in the data set, which is more than any of the other numbers.

A key factor to remember about data sets is that they should always be placed in order. Finding the mode was pretty simple in this instance, but if the numbers were scrambled like before things would be a lot more difficult. Ordering the numbers is the first thing you should do when you’re doing any sort of descriptive statistics.

The final part of descriptive statistics that you will learn about is finding the mean or the average. The average is the addition of all the numbers in the data set and then having those numbers divided by the number of numbers within that set. Let’s look at the following data set. 6, 7, 13, 15, 18, 21, 21, and 25 will be the data set that we use to find the mean. Now in this data set there are 8 numbers. The first thing we will do is add together all of the numbers within the set.

6 + 7 + 13 + 15 + 18 + 21 + 21 + 25 = 126

Now we divide 126 by the number of numbers in the set 8, and we get the result. You should have gotten 15.75 as the mean for this set of data.

In terms of measures of central tendency, this is all there is to descriptive statistics. To make it easier, you can try to learn about the different statistics formulas for mean, median, and mode.

The Second Type of Descriptive Statistics 

The other type of descriptive statistics is known as the measures of spread. This type of statistics is used to analyze the way the data spread out, such as noticing that most of the students in a class got scores in the 80 percentile than in any other area.

One of the most common types of measure of spread is known as the range. The range is incredibly simple to calculate, and it requires just the basic knowledge of math. To calculate the range, simply take the largest number in the data set and subtract the smallest from it. For example, in the set we used to find the average, we will find the range.

25 – 6 = 19

That’s the range for the entire set of data. It’s as easy as that. There are other forms of measures of spread, such as absolute and standard deviation. If you want to learn more about these types of statistics, then check out the Workshop in Probability and Statistics.

Understanding All Forms of Statistics 

Descriptive statistics is only one type. There are several forms of statistical analysis you can perform, such as inferential statistics, which is used to predict what the data may be in the future. Take your first step in inferential statistics by checking out the Udemy course Inferential Statistics in SPSS.