Question

Which of the following variables is not a continuous variable?
A. Distance
B. Height
C. Length
D. Number of cars in a street

Answer 1

Hint: To do this question, we will first have to define what is meant by continuous variables. We will define them as variables which can take any two real values such that they can also take all the real values in that interval, i.e. if ‘x’ is a continuous variable and it can take any two real values, let us assume them to be a and b, where a>b, then x can also take all the values in the interval \[\left[ a,b \right]\]. Then, we will check for these conditions in all the given options and the one which will not fulfill these conditions will be the required answer.

Complete step by step answer:
We here have been asked about continuous variables. To answer this question, we first need to understand what is meant by “continuous variables”.
Now, continuous variables are the variables which can take any two real values such that they can also take all the real values in that interval, i.e. if ‘x’ is a continuous variable and it can take any two real values, let us assume them to be a and b, where a>b, then x can also take all the values in the interval \[\left[ a,b \right]\].
 Now, as here we have to check for continuous variables, we will see if this condition is fulfilled by the given variables or not. And if it is not fulfilled by any one of them, it will not be a continuous variable.
Hence, checking for the given options, we get:
Option-A: distance
Now, we know that distance can take all non-negative real values. So, for distance, according to the above mentioned conditions, if we take $a=0$ and $b=\infty $, then the required interval will be $[0,\infty )$ and we know that distance can take all the values in this interval.
Hence, distance is a continuous variable.
Option-B: height
Now, similarly we know that height can take all non-negative real values. So, for height, according to the above mentioned conditions, if we take $a=0$ and $b=\infty $, then the required interval will be $[0,\infty )$ and we know that height can take all the values in this interval.
Hence, height is a continuous variable.
Option-C: length
Now, similarly we know that length can take all non-negative real values. So, for length, according to the above mentioned conditions, if we take $a=0$ and $b=\infty $, then the required interval will be $[0,\infty )$ and we know that length can take all the values in this interval.
Hence, length is a continuous variable.
Option-D: number of cars in a street
Now, for the number of cars in a street, we know that it can take the values of only natural numbers as it is an object we can count and it is either there or not. So, for number of cars in a street, according to the above mentioned conditions, if we take $a=1$ and $b=2$, then the required interval will be $\left[ 1,2 \right]$ and we know that in this interval, number of cars in a street can either only be 1 or 2 and not any other values in this interval.
Hence, the number of cars in a street is not a continuous function.
Thus, option (D) is the correct option.

Note:
We here have checked for all the options and we obtained the last option as our answer. But if in any case, we obtain an option as an answer which is not the last option, we will still have to check for the next options until all the options have been checked because the question might or might not have one or more correct options. So always check for all the given options.