Basic Statistics

Introduction to statistics

MCQs Basic Statistics Quiz 18

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This post is about the MCQs Basic Statistics Quiz with Answers. There are 20 multiple-choice questions about the Basics of Statistics, covering measures of central tendency (Mean, Median, Mode, Geometric Mean, and Harmonic Mean), Measures of Dispersion, Deviations, Relationships between different measures of central tendency, Coding Methods for computing Mean, etc. Let us start with the MCQs Basic Statistics Quiz.

Online MCQs about Basic Statistics

1. One type of average is

 
 
 
 

2. The coding method is used for calculating

 
 
 
 

3. The arithmetic mean of 5, 9, 12, 15 is

 
 
 
 

4. If 4 is added to all observations in the data then the mean increases by

 
 
 
 

5. The coding method is used for calculating

 
 
 
 

6. The sum of squares of deviations of the values is least when deviations are taken from

 
 
 
 

7. The arithmetic mean of 112, 120, 135, 150, 157 is

 
 
 
 

8. One type of average is

 
 
 
 

9. The mean of the $n$ natural numbers is

 
 
 
 

10. In the case of an Open-end frequency table, the average cannot be computed accurately

 
 
 
 

11. The relation between AM, GM, and HM is

 
 
 
 

12. The sum of absolute deviations of the values is least when deviations are taken from

 
 
 
 

13. If $\Sigma (x – 12) = 0$ then $x=$

 
 
 
 

14. The Geometric Mean of $a$ and $b$ is

 
 
 
 

15. The value obtained by dividing the sum of the values by their number is called

 
 
 
 

16. The arithmetic mean is affected by

 
 
 
 

17. The appropriate average for calculating the average percentage increase in population is

 
 
 
 

18. The sum of deviations of the values from their means is

 
 
 
 

19. If the mean is greater than the mode, the distribution is

 
 
 
 

20. The most central value of an array is called

 
 
 
 

MCQs Basic Statistics Quiz

  • One type of average is
  • The most central value of an array is called
  • In the case of an Open-end frequency table, the average cannot be computed accurately
  • One type of average is
  • The value obtained by dividing the sum of the values by their number is called
  • The arithmetic mean of 5, 9, 12, 15 is
  • The arithmetic mean of 112, 120, 135, 150, 157 is
  • The appropriate average for calculating the average percentage increase in population is
  • The arithmetic mean is affected by
  • The mean of the $n$ natural numbers is
  • The sum of deviations of the values from their means is
  • The sum of squares of deviations of the values is least when deviations are taken from
  • If the mean is greater than the mode, the distribution is
  • If $\Sigma (x – 12) = 0$ then $x=$
  • The Geometric Mean of $a$ and $b$ is
  • The sum of absolute deviations of the values is least when deviations are taken from
  • The coding method is used for calculating
  • The coding method is used for calculating
  • The relation between AM, GM, and HM is
  • If 4 is added to all observations in the data then the mean increases by
  • One type of average is
  • The most central value of an array is called
  • In the case of an Open-end frequency table, the average cannot be computed accurately
  • One type of average is
  • The value obtained by dividing the sum of the values by their number is called
  • The arithmetic mean of 5, 9, 12, 15 is
  • The arithmetic mean of 112, 120, 135, 150, 157 is
  • The appropriate average for calculating the average percentage increase in population is
  • The arithmetic mean is affected by
  • The mean of the $n$ natural numbers is
  • The sum of deviations of the values from their means is
  • The sum of squares of deviations of the values is least when deviations are taken from
  • If the mean is greater than the mode, the distribution is
  • If $\Sigma (x – 12) = 0$ then $x=$
  • The Geometric Mean of $a$ and $b$ is
  • The sum of absolute deviations of the values is least when deviations are taken from
  • The coding method is used for calculating
  • The coding method is used for calculating
  • The relation between AM, GM, and HM is
  • If 4 is added to all observations in the data then the mean increases by
Online MCQs Basic Statistics Quiz with Answers

General Knowledge Quiz, Data Analysis in R Language

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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Online MCQs Basic Statistics 17

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The post is about Online MCQs Basic Statistics with Answers. 20 Multiple-Choice questions covers the topics related to Tables, Frequency Distribution, Measures of Central Tendency, Measure of Dispersion, Coefficient of Variation, Skewness and Kurtosis, etc. Let us start with the Online MCQs Basic Statistics.

Please go to Online MCQs Basic Statistics 17 to view the test

Online MCQs Basic Statistics with Answers

  • If the third moment about mean is zero, the distribution is
  • The first moment about mean is
  • If $b_2=3$ then the distribution is
  • For moderately skewed distribution, the empirical formula holds
  • If $b_2 > 3$ the distribution is
  • The portion of the table containing row captions is called
  • The portion of the table containing column caption is called
  • Title of a table should be in
  • The difference between the upper and lower class boundary is called
  • Class Mark is also called
  • The frequency of the class divided by the total frequency is called
  • The sum of absolute deviations is minimum if these deviations are taken from
  • The measures of dispersion remains unchanged by the change of
  • The measures of dispersion are changed by the change of
  • The standard deviation is independent of change of
  • In Skewed distribution, approximately 95% of cases are falling between
  • If $\overline{x} = 8$ which of the following is minimum?
  • If $x=40$ and $S^2=64$ then the coefficient of variation is
  • The second moment about mean is
  • The average is also called measures of
Online MCQs Basic Statistics Quiz with Answers

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