Continuous Variable

Firstly, know what a variable is to have a better understanding of the continuous variable. Thus, a variable is a numerical expression whose value varies. There exist only 2 kinds of variables i.e. Continuous variable and Discrete variable. Of which, the continuous variable refers to the numerical variable whose value is attained by measuring. The variables can take almost any type of numeric value and can be further divided into meaningful smaller increments which include fractional and decimal values. This, in particular, is a kind of quantitative variable often used in machine learning and statistical modeling to describe data that is measurable in some way. Continuous variables are generally measured on scales such as height, weight, temperature, etc. With the help of continuous variables, one can measure mean, median, variance, or standard deviation. Continuous variables are the ones which in between any two numeric values have an infinite number of values. Different techniques of calculus are used in continuous optimization problems in which the variables are also continuous. 

Types of Continuous Variables

The continuous variables are of two types:

1. Instant variable: The variables that define the level or distance between each category which is equal and static are known as instant variables.

2. Ratio variable: The variables having only one variation from the interval variable are known as ratio variables. The ratio between the score gives the information between the responses regarding the relationship. 

Grab Discrete Variable to Grasp Continuous Variable

As we said above continuous variable meaning is all quantifying the data in some way. To learn about the mechanism, you would need to know more than a little about discrete variables.  So, what does a discrete variable mean? Data that deals with counting is considered to be discrete.  And for all you know, when we count things, we take into account whole numbers like 0, 1, 2, and 3. To better understand the discrete variables, let’s take an example.

Examples of Continuous Variables

Tell us how many eggs a hen lays? A chicken may or may not lay egg/eggs each day, but there are two things that certainly can never happen. There can never be eggs in a negative number, and there can never be a section or a fraction of an egg. 

Now that you know the two variables are distinctive of each other. Then surely, there must be some key differences between the two that set them apart for better description of data.

An example of a continuous variable is temperature as we can have decimals while measuring temperature and it can take on any value in an interval. In nature, almost all the variables present are continuous until the size reaches a quantum level. Therefore, at a macroscopic level, the mass, temperature, energy, speed, length, and so on are all examples of continuous variables. 

Another example of a continuous variable is height. Suppose you want to take an accurate measurement of your height and you are having the most advanced device in the world. You already know that you are between 150 and 152 cm but you want to know the accurate number. At first measurement, the device reads 151.2, then you measure it again and now the device reads 152.21. This means that even in between 150 and 152 there is an infinite number of possibilities.

Continuous Variables vs. Discrete Variables:

A variable holding any value between its maximum value and its minimum value is what we call a continuous variable; otherwise, it is called a discrete variable.

Step 1: First thing to do is to discover how long it would take you to count out the possible values of your variable. For instance, if your variable is “Temperature in North India”. See to it as how long would it take you to find every possible temperature reading? It would literally take you a lifetime.

45°, 47.11° 48.4°, 49.11°, 49.111°,…

For variables like these where you begin counting now and end up never (i.e. the numbers go on and until eternity), you have what’s known as a continuous variable.

If your variable is “Number of palm trees in a nursery,” then you can literally count all of the numbers (there can’t be innumerable numbers of palm trees). And with that, you have what’s called a discrete variable.

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Difference Between Discrete and Continuous Variables

Solved Examples

For the below given cases, identify whether a continuous random or discrete variable is involved?

Case 1

The length of a polar bear

Answer: The length is essentially treated as a continuous variable, since a polar bear will precisely not measure 3m. Even, the length of an adult male may measure between 2.4-3m, while reaching above 3m (more than 10 feet). That said, the length will vary by some foot or a fraction and thus is a continuous variable.

Case 2

The age of a polar bear

Answer: Age can every so often be considered as continuous or discrete variable. For example, we usually depict age as only a number of years, but occasionally we discuss a polar bear being to live beyond 18-20years old. Technically, since age can be regarded as a continuous random variable, then that is what it is reviewed, unless we have logic to deal with it as a discrete variable.

Now let’s take a fun quiz to know how far you have discrete and continuous variables.

Fun Quiz

For 1-10, find out whether each condition is a continuous or a discrete random variable, or if it is none

Did You Know

A variable in algebra is not quite alike to a variable in statistics.

Continuous Variables – Some more Solved Examples

1. Is bodyweight an example of a continuous variable?

Solution: Yes, bodyweight is an example of a continuous variable.

2. Is gender an example of a continuous variable?

Solution: No, gender is not an example of a continuous variable; however, it is a discrete variable.

3. How many gallons of milk does a cow give and is this an example of a continuous variable?

Solution: Cow’s milk is another example of a continuous variable. Although the amount of milk it gives daily varies, one day the cow can give 2.89 gallons, and the other day it can give 4 gallons. Therefore, there is an infinite number of possibilities which includes decimals and fractions as well.