Question

State which of the following variables are continuous and which are discrete:
a) number of children in your class
b) distance travelled by a car
c) sizes of shoes
d) time
e) number of patients in a hospital

Answer 1

Hint: In order to solve this question, firstly we will see what is the main difference between a continuous variable and a discrete variable. After that, we will analyse every option and state accordingly which one is a continuous variable and which one is a discrete variable.

Complete step by step solution:
Before we solve this question, let us understand what are variables and what are types of variables. Variables are the unspecified term of the equation, formula, or we can theory. It is basically an unspecified numeric.
A variable may be continuous or discrete. If a variable can take two particular real values such that it can also take on all real values between them, then the variable is said to be continuous, whereas if variables are countable in a finite amount of time, then the variables are said to be discrete variables.
Now, let us analyse options one by one.

A.So, the first option is “number of children in your class”.
Now, in a class the number of children will be the same for any number of times without any change, so we can count the number of children easily.
Hence, it is a discrete variable.

B.The second option is given as “distance travelled by a car”.
So, we know that the distance can take all non-negative real values.
Hence, it is a continuous variable.

C.Now, the third option is “sizes of shoes”
So, we know that it takes only natural numbers and fixed numbers increasing in a particular amount. Because we generally say people wear a size or size So we count the size of shoes easily.
Hence, it is a discrete variable

D.Now the fourth option is “time”
It is a continuous variable. Like for example, time taken by an athlete. An athlete can improve the time taken to complete the race. So, there is no fixed time, which can be calculated for an athlete to complete a race.
Hence, it is a continuous variable.

E.The fifth option is “number of patients in a hospital”
Now for the number of patients we know that it can have only natural values as we can count them.
Hence, it is a discrete variable.

Hence, we get the result as:
a) number of children in your class: Discrete variable
b) distance travelled by a car: Continuous variable
c) sizes of shoes: Discrete variable
d) time: Continuous variable
e) number of patients in a hospital: Discrete variable

Note: Sometimes students get confused between the discrete or continuous variable. So, to solve such problems it is necessary to understand the definitions of both the terms. And also, one important thing is that “time” can be both discrete and continuous. If the time is given in minutes or hours like minutes or hours, in that case we consider it to be a discrete variable because it is a fixed number, and we can count. But if the “time” is given in general or like time taken by a person or something, then we consider it as a continuous variable.