Important Random Variable MCQ 2

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The post is about the Random Variable MCQ Test. There are 20 multiple-choice questions about random variables. The quiz covers topics related to the basic concept of random variables, real-life examples of random variables, random experiments, types of random variables, and distribution of random variables. Let us start the quiz random variable MCQ Test.

Online MCQs about Random Variables with Answers

1. A variable whose value is determined by the outcome of a random experiment is called

 
 
 
 

2. The speed of the car is an example of

 
 
 
 

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

 
 
 
 

4. The sum of probabilities of a discrete random variable is

 
 
 
 

5. If $X$ is a uniform variate $U(5, 10)$ then the mean of $X$ is

 
 
 
 

6. The observed value of a statistic is:

 
 
 
 

7. If $X$ and $Y$ are random variables then $E(X+Y)$ is equal to

 
 
 
 

8. If $x$ is a discrete random variable, the function $f(x)$ is

 
 
 
 

9. Height measurements of 50 students studying in a college

 
 
 
 

10. A variable which can assume each and every value within a given range is called

 
 
 
 

11. A random variable assuming only a finite number of values is called:

 
 
 
 

12. A random variable is also called

 
 
 
 

13. The lifetime of a car tire is

 
 
 
 

14. A random variable assuming an infinite number of values is called

 
 
 
 

15. The number of students in a class is an example of

 
 
 
 

16. If $X\sim N(\mu, \sigma^2)$ and $a$ and $b$ are real numbers, then the mean of $(aX+b)$ is

 
 
 
 

17. Random numbers can be generated mechanically by

 
 
 
 

18. A chi-square random variable can assume the value:

 
 
 
 

19.

If $X$ is a uniform variate $U(5, 10)$ then the variance of $X$ is

 
 
 
 

20. Suppose, four coins are tossed, the value of a random variable $H$ (No. of heads) is:

 
 
 
 

Online Random Variable MCQ Test

Online Random Variable MCQs with Answers
  • A random variable is also called
  • A random variable assuming only a finite number of values is called:
  • A random variable assuming an infinite number of values is called
  • The number of students in a class is an example of
  • The speed of the car is an example of
  • Random numbers can be generated mechanically by
  • Suppose, four coins are tossed, the value of a random variable $H$ (No. of heads) is:
  • A quantity which can vary from one individual to another is called
  • A variable which can assume each and every value within a given range is called
  • The lifetime of a car tire is
  • Height measurements of 50 students studying in a college
  • A variable whose value is determined by the outcome of a random experiment is called
  • If $x$ is a discrete random variable, the function $f(x)$ is
  • If $X$ and $Y$ are random variables then $E(X+Y)$ is equal to
  • The sum of probabilities of a discrete random variable is
  • A chi-square random variable can assume the value:
  • The observed value of a statistic is:
  • If $X$ is a uniform variate $U(5, 10)$ then the mean of $X$ is
  • If $X$ is a uniform variate $U(5, 10)$ then the variance of $X$ is
  • If $X\sim N(\mu, \sigma^2)$ and $a$ and $b$ are real numbers, then the mean of $(aX+b)$ is
Random Variable MCQ Test

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Quartiles

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Introduction to Quantiles and Quartiles

Quantiles are the techniques used to divide the data into different equal parts. For example, quantiles divide the data into four equal parts. Quartile comes from quarter which means 4th part. Deciles divide the data into ten equal parts and they come from deca means the 10th part. Percentiles divide the data into hundred parts and it comes to percent which means the 100th part.

Therefore, quartiles, deciles, and percentiles are used to divide the data into 4, 10, and 100 parts respectively. The quantiles, deciles, and percentiles are collectively called quantiles.

Quartiles

Quartiles are the rules that divide the data into four equal parts. When we divide any data into four equal parts, we cut it at equidistant points. The quartiles ($Q_1, Q_2$, and $Q_3$) divide the data into four equal parts, so divide the number of observations by four for each quartile.

Quartiles for Ungroup Data

\begin{align*}
Q_1 &= \left(\frac{n+1}{4}\right)th \text{ value is the} \frac{1}{4} \text{ part}\\
Q_2 &= \left(\frac{2(n+1)}{4}\right)th \text{ value is the} \frac{2}{4} \text{ part}\\
Q_3 &=\left(\frac{3(n+1)}{4}\right)th \text{ value is the} \frac{3}{4} \text{ part}
\end{align*}

The following ungroup data has 96 observations $(n=96)$

222225253030303131333639
404042424848505152555759
818689899091919192939393
939494949596969697979898
999999100100100101101102102102102
102103103104104104105106106106107108
108108109109109110111112112113113113
113114115116116117117117118118119121

The first, second, and third quartiles of the above data set are:

\begin{align*}
Q_1 &= \left(\frac{n}{4}\right)th \text{ position } = \left(\frac{96}{4} = 24\right)th \text{ value} = 59\\
Q_2 &= \left(\frac{2\times 96}{4}\right) = 48th \text{ position} = 98\\
Q_3 &= \left(\frac{3\times n}{4}\right)th = \left(\frac{3\times 96}{}\right)th \text{ position} = 72th \text{ position} = 108
\end{align*}

Note that the above data is already sorted. If the data is not sorted, we first need to arrange/sort it in ascending order.

Quartiles for Gruoped Data

One can also compute the quantiles for the following grouped data, hence the quartiles.

ClassesfxC.B.CF
65-84974.564.5-84.59
85-1041094.584.5-104.519
105-12417114.5104.4.5-124.536
125-14410134.5124.5-144.546
145-1645154.5144.5-164.551
165-1844174.5164.5-184.455
185-2045194.5184.5-204.560
Total60   

From the above-grouped data, we have 60 observations $(n=60)= \sum\limits_{i=1}^n = f_i = \Sigma f = 60$. The three quartile will be

\begin{align*}
\frac{n}{4} &= \left(\frac{60}{4}\right)th = 15th \text{ value}\\
Q_1 &= l + \frac{h}{f}\left(\frac{n}{4} – CF\right) = 84.5 + \frac{20}{10}(15-9) = 96.5\\
\frac{2n}{4} &= \left(\frac{2\times 60}{4} \right) = 30th \text{ value}\\
Q_2 &= l + \frac{h}{f}\left(\frac{2n}{4} – CF\right) = 104.5 + \frac{20}{17}(30-19) = 117.44\\
\frac{3n}{4} &= \left(\frac{3\times 60}{4} \right) = 45th \text{ value}\\
Q_3 &= l + \frac{h}{f}\left(\frac{3n}{4} – CF\right) = 124.5 + \frac{20}{17}(45-36) = 142.5\\
\end{align*}

Frequently Asked Questions about Quantiles

  1. Define Quartiles, Deciles, Percetiles.
  2. What are fractiles or Quantiles?
  3. How quantiles are computed for grouped and ungrouped data.

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Important MCQs Index Numbers Quiz 5

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The post is about the MCQs Index Numbers Quiz. There are 20 multiple-choice questions covering the topics related to simple and weighted index numbers, retail price index numbers, consumer price index numbers, average and aggregate index numbers, and chain base index numbers. Let us start with MCQs Index Numbers Quiz.

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MCQs Index Numbers Quiz

  • Express the following average weekly wages as index numbers with base 1998 to 1 dp
  • Base year weighted index numbers are
  • Current year quantities are used as weights in
  • Paasche’s price index number is
  • The index number given by $\frac{\Sigma p_nq_0}{\Sigma p_0q_0}\times 100$ is
  • If $\Sigma p_1q_0=403$, $\Sigma p_0q_0=283$, then index number is
  • Fisher’s index number is ————- of Laspeyres and Paasche’s index numbers
  • Computing methods of consumer price index are
  • Retail price index numbers are also called
  • Another name for consumer price index number is
  • The aggregate expenditure method and family budget method give
  • Which method of construction of CPI number is the Laspeyres index number
  • In 2000, the retail price index was 178 with 1990 = 100. Convert a weekly wage of $400 back to 1990 constant prices, giving your answer correct to the nearest penny.
  • Complete the following table which shows two index number series being spliced together to give a single series based on 1997. Give your answers correct to one dp.
  • Complete the following table in which a chain-based index is being converted to one with a fixed base 1997. Give your answers correct to one decimal place.
  • You are assisting with the work on a maintenance department’s budget for the next quarter of 2000. The maintenance department’s budget for the current quarter (just ending) is $200,000. Its use of materials, and their respective prices, are shown below. You require an all-item price index for materials for the next quarter, using the current quarter as a base and the current quantities as weights. Complete the table by filling in the appropriate numerical value in the spaces indicated by the letters.
  • Calculate the required index, using the formula $100\times \left(\frac{\Sigma wP_1}{\Sigma wP_0}\right)$ giving your answer to one dp.
  • If the price index ($100\times \left(\frac{\Sigma wP_1}{\Sigma wP_0}\right)$) calculated was 104, estimate the budget for the next quarter, giving your answer to the nearest $\$000$. You are assisting with the work on a maintenance department’s budget for the next quarter of 2000. The maintenance department’s budget for the current quarter (just ending) is $\$200,000$. Its use of materials, and their respective prices, are shown below.  
  • If a price index is 104, which of the following statements is/are correct about average prices?  
  • Which of the following statements about the base time is/are correct?
Statistics MCQs Index Numbers Quiz

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