MCQs Discrete Probability Distributions 7

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The post is about MCQs Discrete Probability Distributions. There are 20 multiple-choice questions about discrete probability distributions covering distributions such as Binomial Probability Distribution, Bernoulli Probability Distribution, Poisson Probability Distribution, Poisson Probability, Distribution, Geometric Probability Distribution, and Hypergeometric Probability Distribution. Let us start with the MCQs Discrete Probability Distributions Quiz.

Online MCQs about Discrete Probability Distributions

1. The mode of the geometric distribution is

 
 
 
 

2. The probability of success changes from trial to trial in

 
 
 
 

3. Which of the following could never be described by the Binomial distribution?

 
 
 
 

4. If $X$ is the number of trials for the negative binomial distribution with parameters $p$ and $k$ then its minimum value is

 
 
 
 

5. The hypergeometric random variable is a

 
 
 
 

6. For a binomial distribution which of the following is true

 
 
 
 

7. Which of the following is a characteristic of the probability distribution for any random variable

 
 
 
 

8. The probability of success does not change from trial to trial in

 
 
 
 

9. Suppose, we have a Poisson distribution with $\lambda$ equal to 2 then the probability of having exactly 10 occurrences is

 
 
 
 

10. The successive trials are without replacement in

 
 
 
 

11. The parameters of hypergeometric distribution are

 
 
 
 

12. In what case would the Poisson distribution be a good approximation of the binomial distribution

 
 
 
 

13. For a given binomial distribution with $n$ fixed if $p=0.5$ then

 
 
 
 

14. In a Binomial distribution, if $n$ is the number of trials and $p$ is the probability of success, then the mean value is given by

 
 
 
 

15. Which of the following is the most reasonable condition for the binomial approximation to the hypergeometric distribution?

 
 
 
 

16. The necessary and sufficient condition of the hypergeometric distribution is

 
 
 
 

17. In a binomial probability distribution, the sum of the probability of failure and the probability of success is always

 
 
 
 

18. The number of possible outcomes in a Bernoulli trial is

 
 
 
 

19. The mean and mode of the Binomial distribution are equal if

 
 
 
 

20. The binomial distribution may be approximated by a Poisson distribution if

 
 
 
 

MCQs Discrete Probability Distributions

  • For a binomial distribution which of the following is true
  • The number of possible outcomes in a Bernoulli trial is
  • The mean and mode of the Binomial distribution are equal if
  • The hypergeometric random variable is a
  • The parameters of hypergeometric distribution are
  • The probability of success changes from trial to trial in
  • The probability of success does not change from trial to trial in
  • The successive trials are without replacement in
  • Which of the following could never be described by the Binomial distribution?
  • If $X$ is the number of trials for the negative binomial distribution with parameters $p$ and $k$ then its minimum value is
  • For a given binomial distribution with $n$ fixed if $p=0.5$ then
  • The necessary and sufficient condition of the hypergeometric distribution is
  • Which of the following is the most reasonable condition for the binomial approximation to the hypergeometric distribution?
  • Suppose, we have a Poisson distribution with $\lambda$ equal to 2 then the probability of having exactly 10 occurrences is
  • Which of the following is a characteristic of the probability distribution for any random variable
  • In what case would the Poisson distribution be a good approximation of the binomial distribution
  • The mode of the geometric distribution is
  • The binomial distribution may be approximated by a Poisson distribution if
  • In a Binomial distribution, if $n$ is the number of trials and $p$ is the probability of success, then the mean value is given by
  • In a binomial probability distribution, the sum of the probability of failure and the probability of success is always
MCQs Discrete Probability Distributions

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Quartile Deviation (2025)

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Quartile deviation denoted by QD is the absolute measure of dispersion and it is defined as the half of the difference between the upper quartile ($Q_3$) and the lower quartile ($Q_1$).

The Quartile Deviation also known as semi-interquartile range (Semi IQR), is a measure of dispersion that focuses on the middle 50% of the data. It is calculated as half the difference between the Third Quartile ($Q_3$) and the First Quartile ($Q_1$). One can write it mathematically as

$$QD = \frac{Q_3-Q_1}{2}$$

Note that the interquartile range is only the difference between the upper quartile ($Q_3$) and the lower quartile ($Q_1$), that is,

$$Interquartile\,\, Range = IRQ = Q_3 – Q_1$$

The Relative Measure of Quartile Deviation is the Coefficient of Quartile Deviation and is given as

$$Coefficient\,\,of\,\,QD = \frac{Q_3 – Q_1}{Q_3 + Q_1}\times 100$$

Quartile Deviation

When to Use QD

  • When dealing with skewed data or data with outliers.
  • When a quick and easy measure of dispersion is needed.

Interpretation QD

Spread: A larger quartile deviation indicates greater variability in the middle portion of the data.
Outliers: QD is less sensitive to extreme values (outliers) compared to the standard deviation.

Quartile Deviation for Ungrouped Data

222225253030303131333639
404042424848505152555759
818689899091919192939393
939494949596969697979898
999999100100100101101102102102102
102103103104104104105106106106107108
108108109109109110111112112113113113
113114115116116117117117118118119121

The above data is already sorted and there are a total of 96 observations. The first and third quartiles of the data can be computed as follows:

$Q_1 = \left(\frac{n}{4}\right)th$ value $= \left(\frac{96}{4}\right)th$ value $= 24th$ value. The 24th observation is 59, therefore, $Q_1=59$.

$Q_3 = \left(\frac{3n}{4}\right)th$ value $= \left(\frac{3\times 96}{4}\right)th$ value $= 72th$ value. The 72nd observation is 108, therefore, $Q_3=108$.

The quartile deviation will be

$$QD=\frac{Q_3 – Q_1}{2} = \frac{108-59}{2} = 24.5$$

The Interquartile Range $= IQR = Q_3 – Q_1 = 108 – 59 = 49$

The coefficient of Quantile Deviation will be

$$Coefficient\,\, of\,\, QD = \frac{Q_3 – Q_1}{Q_3 – Q_1}\times 100 = \frac{108-59}{108+59}\times 100 = 29.34\%$$

Quartile Deviation for Grouped Data

Consider the following example for grouped data to compute the quartile deviation.

ClassesFrequenciesClass BoundariesCF
11-14.91110.95-14.9511
15-20.91914.95-20.9530
21-24.92120.95-24.9551
25-30.93424.95-30.9585
31-34.91630.95-34.95101
35-40.9934.95-40.95110
41-44.9440.95-44.95114
Total114  

The first and third quartiles for the above-grouped data will be

\begin{align*}
Q_1 &= l + \frac{h}{f}\left(\frac{n}{4} – C\right)\\
&= 14.95 + \frac{6}{19}\left(\frac{114}{4} – 11\right)\\
&= 14.95 + \frac{6}{19}(28.5 – 11) = 20.48\\
Q_3 &= l + \frac{h}{f}\left(\frac{3\times 114}{4}-85\right)\\
&=30.95 + 0.187418 = 31.14
\end{align*}

The QD is

$$QD = \frac{Q_3 – Q_1}{2} = \frac{31.14 – 20.48}{2} = \frac{10.66}{2} = 5.33$$

The Interquartile Range will be

$$IQR = Q_3 – Q_1 = 31.14 – 20.48 = 10.66$$

The coefficient of quartile deviation is

$$Coefficient\,\,of\,\, QD = \frac{Q_3 – Q_1}{Q_3 + Q_1}\times 100 = \frac{31.14 – 20.48}{31.14+20.48}\times 100 = 20.65\%$$

  • Less affected by outliers: Makes it suitable for skewed data.
  • Easy to calculate: Relatively simple compared to standard deviation.

Disadvantages of QD

  • Ignores extreme values: This may not provide a complete picture of the data’s spread.
  • Less sensitive to changes in data: Compared to standard deviation.

In summary, Quartile deviation is a valuable and useful tool for understanding the spread of data, particularly when outliers are present. By focusing on the middle 50% of the data, it provides a robust measure of dispersion that is less sensitive to extreme values. However, it is important to consider its limitations, such as its insensitivity to outliers and changes in data.

Frequently Asked Questions about Quartile Deviation

  1. What is quartile deviation?
  2. What are the advantages of QD?
  3. What are the disadvantages of QD?
  4. What is IQR?
  5. What is Semi-IQR?
  6. How QD is interpreted?
  7. How QD is computed for grouped and ungrouped data?
  8. When QD should be used?

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MCQs Cluster Analysis Quiz 6

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The post is about MCQs cluster Analysis. There are 20 multiple-choice questions from clustering, covering topics such as k-means, k-median, k-means++, cosine similarity, k-medoid, Manhattan Distance, etc. Let us start with the MCQs Cluster Analysis Quiz.

Please go to MCQs Cluster Analysis Quiz 6 to view the test

Online MCQs Cluster Analysis

  • Which of the following statements is true?
  • What are some common considerations and requirements for cluster analysis?
  • Which of the following statements is true?
  • Which of the following statements is true?
  • Which of the following statements about the K-means algorithm are correct?
  • Which of the following statements, if any, is FALSE?
  • In the figure below, Map the figure to the type of link it illustrates.
  • In the figure below, Map the figure to the type of link it illustrates.
  • In the figure below, Map the figure to the type of link it illustrates.
  • Considering the k-median algorithm, if points $(-1, 3), (-3, 1),$ and $(-2, -1)$ are the only points that are assigned to the first cluster now, what is the new centroid for this cluster?
  • Which of the following statements about the K-means algorithm are correct?
  • Given the two-dimensional points (0, 3) and (4, 0), what is the Manhattan distance between those two points?
  • Given three vectors $A, B$, and $C$, suppose the cosine similarity between $A$ and $B$ is $cos(A, B) = 1.0$, and the similarity between $A$ and $C$ is $cos(A, C) = -1.0$. Can we determine the cosine similarity between $B$ and $C$?
  • Is K-means guaranteed to find K clusters that lead to the global minimum of the SSE?
  • The k-means++ algorithm is designed to better initialize K-means, which will take the farthest point from the currently selected centroids. Suppose $k = 2$ and we have chosen the first centroid as $(0, 0)$. Among the following points (these are all the remaining points), which one should we take for the second centroid?
  • Which of the following statements is true?
  • Suppose $X$ is a random variable with $P(X = -1) = 0.5$ and $P(X = 1) = 0.5$. In addition, we have another random variable $Y=X * X$. What is the covariance between $X$ and $Y$?
  • For k-means, will different initializations always lead to different clustering results?
  • In the k-medoids algorithm, after computing the new center for each cluster, is the center always guaranteed to be one of the data points in that cluster?
  • In the k-median algorithm, after computing the new center for each cluster, is the center always guaranteed to be one of the data points in that cluster?
MCQs Cluster Analysis Quiz with Answers

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