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Random variable and its types - class-XII

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State, which of the following variables are continuous and which are discrete :


Sizes of shoes is discrete
If true then enter $1$ and if false then enter $0$

  1. $1$

  2. $0$

  3. Can't determine

  4. None of these


Correct Option: A
Explanation:

Size of a shoe can have integer values only. Hence, it is a discrete variable.

Say true or false:

Sizes of the shoe are discrete variables.

  1. True

  2. False


Correct Option: A
Explanation:

Size of shoe can have have only integer value. Hence, it is a discrete variable.

Are you a girl or boy is an example of ______ variable.

  1. continuous

  2. dependent

  3. discrete

  4. nominal


Correct Option: C
Explanation:

A discrete variable is a variable whose value is obtained by counting.
So, are you a girl or boy is an example of discrete variable.
Since it is answerable.

Which one of the statement is discrete variable?

  1. weight of animals in zoo

  2. distance travelled between colleges

  3. number of heads by flipping a coins

  4. height of animals in park


Correct Option: C
Explanation:

Discrete variables are countable in a finite amount of time.
So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.

The statement "number of heads when flipping a coin" is an example of ______ variable.

  1. continuous

  2. dependent

  3. discrete

  4. nominal


Correct Option: C
Explanation:

Discrete variables are countable in a finite amount of time.
So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.

Which variables are countable in a finite amount of time?

  1. dependent

  2. continuous

  3. nominal

  4. discrete


Correct Option: D
Explanation:

Discrete variables are countable in a finite amount of time.
Example: Count the number of people in your home.

How many times will you brush your teeth. The answer is an example of which type of variable?

  1. continuous

  2. dependent

  3. nominal

  4. discrete


Correct Option: D
Explanation:

A discrete variable is a variable whose value is obtained by counting.
So, how many times will you brush your teeth is countable.

______ is not a discrete variable.

  1. average mark of a student

  2. what is your age?

  3. shoe size

  4. weight of a dog


Correct Option: D
Explanation:

Weight of a dog is not a discrete variable.
Because, the weight of a dog is a continuous variable as it can take any value - for example, $2$ kg, $5$ kg, $4.2$ kg etc.

Teacher asked a student to state how many times in the last month they visited their family doctor. The answer is an example of which type of variable?

  1. continuous

  2. dependent

  3. discrete

  4. nominal


Correct Option: C
Explanation:

A discrete variable is a variable whose value is obtained by counting.
So, here the student can able to say how many times he visited the doctor.
Therefore, the given statement is discrete.

Count the number of students in a class is an example of ________ variable.

  1. dependent

  2. continuous

  3. nominal

  4. discrete


Correct Option: D
Explanation:

Discrete variables are countable in a finite amount of time.
So, counting a number of students in a class is an example of discrete variable.
Because we can easily count the number of students in a class.

Find the discrete variable.

  1. number of chocolates in a box

  2. time taken by an athlete

  3. height of a student in a class

  4. weight of animals in zoo


Correct Option: A
Explanation:

Discrete variables are countable in a finite amount of time.
So, number of chocolates in a box is an example of discrete variable.
Because we can easily count the number of chocolate in a box.

______ variables measured with enough precision can often be considered continuous for practical purposes.

  1. continuous

  2. discrete

  3. nominal

  4. none of the above


Correct Option: B
Explanation:

A discrete variable is a variable whose value is obtained by counting.
So, discrete variables measured with enough precision can often be considered continuous for practical purposes.
Example: number of students absent in a class.

Which variable has the infinite set of the data?

  1. dependent

  2. nominal

  3. discrete

  4. continuous


Correct Option: D
Explanation:

Continuous variable has the infinite set of the data.
Example: Time taken to write a homework.

The length of someone's foot is an example of _______ variable.

  1. continuous

  2. discrete

  3. dependent

  4. nominal


Correct Option: A
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
So, the length of someone's foot is an example of continuous variable.

______ is not a continuous variable.

  1. are you a girl or boy?

  2. weight of a goat

  3. measure the height of a student

  4. time taken to complete a task


Correct Option: A
Explanation:

Continuous variable has the infinite set of the data.
So, are you a girl or boy is not an example of continuous variable.

The weight of students in a class is an example of ________ variable.

  1. discrete

  2. continuous

  3. dependent

  4. nominal


Correct Option: B
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
So, The weight of students in a class is an example of continuous variable.

The height of animals in park is not a _______ variable.

  1. discrete

  2. dependent

  3. nominal

  4. continuous


Correct Option: A
Explanation:

A discrete variable is a variable whose value is obtained by counting.
So, height of animals in a park is not a discrete variable. 
Because the height will not be same for all animal, it may varying in height. 
example: elephant - $4$ m, tiger - $2$ m, giraffe - $10$ m

What type of variable is this?
Number of bubbles in a fish tank.

  1. dependent

  2. continuous

  3. nominal

  4. discrete


Correct Option: D
Explanation:

A discrete variable is a variable whose value is obtained by counting.
So, number of bubbles in a fish tank is countable.

A _______ variable is a variable whose value is obtained by measuring.

  1. dependent

  2. continuous

  3. discrete

  4. nominal


Correct Option: B
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
Example: The weight of a cat is a continuous variable as it can take any value - for example, $2$ kg, $4$ kg, $3.2$ kg etc.

What type of variable is given below?
distance travelled from classes.

  1. discrete

  2. dependent

  3. nominal

  4. continuous


Correct Option: D
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
So, distance travelled from classes is an example of continuous variable.

The height of animals in park is a _______ variable.

  1. discrete

  2. continuous

  3. nominal

  4. dependent


Correct Option: B
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
The height of animals in park is a continuous variable.
Because the animals have different heights.

Which one of the following is a continuous variable statement?

  1. how old are you?

  2. number of students in a class

  3. weight of a new born

  4. count the number of chocolates in a jar


Correct Option: C
Explanation:

Continuous variable has the infinite set of the data.
So, weight of a newborn is an example of continuous variable.
Because the weight may vary from $2.3$ kg, $3.1$ kg, $4$ kg etc.

Time taken to complete a task. The answer is an example of which type of variable?

  1. discrete

  2. dependent

  3. continuous

  4. nominal


Correct Option: C
Explanation:

Continuous variable has the infinite set of the data.
So, time taken to complete a task is an example of continuous variable.
For example time taken to complete a task will be $1$ minute $10$ seconds, $1$ minute $20$ seconds, and so on.

Continuous variable has the ______ set of the data.

  1. finite

  2. infinite

  3. composite

  4. definite


Correct Option: B
Explanation:

Continuous variable has the infinite set of the data.
Example: height of students in a class
Each and every students in a class has different heights, like $56.5, 45.9, 67.8$ etc..

Example of continuous variable is ________.

  1. number of bubbles in a fish tank

  2. time taken to complete a task

  3. are you a girl or boy?

  4. toss a coin to get head


Correct Option: B
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
So, time taken to complete a task is a continuous variable as it can take any value - for example, $2$ hours $2$ mins, $2$ hours $20$ seconds etc..

Measurement of time, distance or weight are examples of ________ variable.

  1. discrete

  2. nominal

  3. continuous

  4. none of the above


Correct Option: C
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
Example: 
The weight of a cat is a continuous variable as it can take any value - for example, $3.4$ kg, $3.5$ kg, $4.01$ kg, etc.

The statement "weight of a cow" is an example of ______ variable.

  1. continuous

  2. discrete

  3. dependent

  4. nominal


Correct Option: A
Explanation:

Continuous variable has the infinite set of the data.
So, weight of a cow is a continuous variable.
Since the weight can be measured in $3.5$ kg, $12.05$ kg, $12.5$ kg, $37.9$ kg etc..

Identify the continuous statement.

  1. toss a coin to get head

  2. are you a girl or boy?

  3. weight of animals in zoo

  4. number of bubbles in a fish tank


Correct Option: C
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
So, weight of animals in zoo is a continuous variable as it can take any value - for example, $3$ kg, $3.567$ kg, $4.01$ kg, etc.

Which one of the following variable is not a continuous variable?

  1. distance

  2. height

  3. length

  4. number of cars in a street


Correct Option: D
Explanation:

A continuous variable is a variable whose value is obtained by measuring.
So, distance, height and length are continuous variable.
Therefore, number of cars in a  street is not a continuous variable.

Sizes of shoe are which types of variables?

  1. discrete

  2. random

  3. continous

  4. nominal


Correct Option: A
Explanation:

There are two types of variables. Discrete and continuous. 

To explain by example, the set of real numbers is continuous, between any two distinct real numbers there exist infinite real numbers. Between 1.2 and 1.3 there exists 1.24 and so many more. 
The set of natural numbers on the other hand, constitutes a discrete sample space. 
Due to the limitations posed by manufacturing tools, we can only produce shoes of varying sizes in discrete steps.

The mean of discrete obervations $y _1, y _2$ , ................ , $y _n$ is given by

  1. $\displaystyle \frac{\sum _{i=1}^{n} y _i}{n}$

  2. $\displaystyle \frac{\sum _{i=1}^{n} y _i}{\sum _{i=1}^{n}i}$

  3. $\displaystyle \frac{\sum _{i=1}^{n} y _i f _i}{n}$

  4. $\displaystyle \frac{\sum _{i=1}^{n} y _i f _i}{\sum _{i=1}^{n}y _if _i}$


Correct Option: A
Explanation:

Mean of terms = $\dfrac{Sum}{number}$


Therefore, Mean = $\displaystyle \dfrac{\sum _{i=1}^{n} y _i}{n}$

Number of patients in a hospital are discrete variable


If true then enter $1$ and if false then enter $0$

  1. $1$

  2. $0$

  3. can't determine

  4. None of these


Correct Option: A

Distance travelled by a car is a continuous variable
If true then choose $1$ and if false then choose $0$

  1. $1$

  2. $0$

  3. $4$

  4. none of the above


Correct Option: A
Explanation:

The distance travelled by a car can be a fraction hence it is a continuous variable

Hence, option (A) is correct

Sizes of shoes are discrete variables,

If true then enter $1$ and if false then enter $0$

  1. Varies from case to case

  2. $0$

  3. $1$

  4. None of these


Correct Option: C
Explanation:

Size of a shoe can have values only in natural numbers. Hence, it is a discrete variable.

Hence, option (C) is correct

A quantity which can vary from one individual to another is called a variable.


If true then enter $1$ and if false then enter $0$

  1. $0$

  2. $1$

  3. can't determine

  4. None of these


Correct Option: B
Explanation:

A quantity which can vary from one individual to another is called a variable.

The variable number of children in your class is discrete variable

  1. True

  2. False

  3. can't determine

  4. none of these


Correct Option: A
Explanation:

Number of children in the class can be counted and it will take value only as a whole number. Hence, it is a discrete variable.

The sizes of shoes is a continuous variable
If true then enter $1$ and if false then enter $0$

  1. $1$

  2. $0$

  3. $10$

  4. None of these


Correct Option: B
Explanation:

Size of a shoe can have integer values only. Hence, it is a discrete variable.

Time is continuous variable
If true then enter $1$ and if false then enter $0$

  1. $1$

  2. $0$

  3. $3$

  4. None of these


Correct Option: A
Explanation:

Time can have any value including integers and rational numbers. Hence, it is a continuous variable.

State, which of the following variables are continuous and which are discrete :


Daily temperature of a city is continuous
If true then enter $1$ and if false then enter $0$

  1. Can't determine

  2. $0$

  3. $1$

  4. None of these


Correct Option: C
Explanation:

Temperature of a city can have any value including integers and rational numbers. Hence, it is a continuous variable.

State, which of the following variables are continuous and which are discrete :

Marks scored in a text is discrete
If true then enter $1$ and if false then enter $0$

  1. $1$

  2. $0$

  3. Can't determine

  4. None of these


Correct Option: A
Explanation:

Marks scored in a test can have have only integer value. Hence, it is a discrete variable.

Daily temperature is continuous variable.

If true then enter $1$ and if false then enter $0$

  1. $1$

  2. $0$

  3. Can't determine

  4. None of these


Correct Option: A
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