Measures of Dispersion

Measures of Dispersion is a part of Statistics through which we can understand data variability. Statistical dispersion shows how scattered the variable is, and the numerical data vary about an average value. The study of the dispersion measurement helps to understand the distribution of data. 

Measurement of Dispersion is important in statistics to understand data variation around a central value. Mean, Standard Deviation; Variance is the measure used to calculate dispersion. To understand and analyze the topic of Measures of dispersion, some important MCQS are given related to this topic. Post each question; the answers are also given for your reference.

Measures of Dispersion MCQs:

Q1. A study in Statistics that helps to interpret the variability of data is knowns as _________

1. 1. Standard Deviation
   2. The measurer of Central tendency
   3. The measurer of dispersion
   4. None of the above

Ans: C. Measure of Dispersion

Q2. Which Measures of Dispersion are used to compare the distribution of two or more data sets?

1. 1. Absolute Measure of Dispersion
   2. Relative Measure of Dispersion
   3. Coefficient of Dispersion
   4. None of these

Ans: B. A relative measure of Dispersion

Q3. In absolute Measure Of Dispersion, the Square root of variation is known as ________

1. 1. Mean Deviation 
   2. Quartile Deviation
   3. Variance
   4. Standard Deviation

Ans: D. Standard Deviation

Q4.Which of these is simply the difference between the maximum and minimum values given in a data set? 

1. 1. Range
   2. Mean Deviation
   3. Standard Deviation
   4. All of these

Ans: A. Range

Q5. What is the Arithmetic average of the Absolute Deviation of a series called?

1. 1. Coefficient of Mean Deviation
   2. Mean Deviation
   3. Quartile Deviation
   4. Standard Deviation

Ans: B. Mean Deviation

Q6. Are the variations present in the unit of a variable represented by which dispersion method?

1. 1. Coefficient of Variation
   2. A relative measure of dispersion
   3. The absolute measure of dispersion
   4. Measure of dispersion

Ans: C. Absolute Measure of dispersion

Q7. In Statistics of dispersion, the Measure of dispersion can never be __________

1. 1. Positive
   2. Zero
   3. Equal to
   4. Negative

Ans: D. Negative

Q8. In the Absolute Measure of dispersion, the Standard Deviation is always________

1. 1. Zero
   2. Negative
   3. Positive
   4. None of the above

Ans: C. Positive

Q9. On which change the variance of a data set is independent?

1. 1. Origin only
   2. Scale only
   3. Origin and Scale both
   4. None of these

Ans: A. Origin only

Q10.Name the graphical method which helps us investigate the dispersion? 

1. 1. Kinked Curve method
   2. Mean deviation
   3. Standard deviation
   4. Lorenz Curve method

Ans: D. Lorenz Curve method

Q11. In the dispersion study, the relative measure of dispersion is expressed by using.

1. 1. Quartiles
   2. Percentage
   3. Numbers
   4. Same unit

Ans: B . Percentage

Q12. Find the value of the third quartile when the first quartile is 104 and the quartile deviation is 8.

1. 1. 136
   2. 146
   3. 120
   4. 130

Ans: C. 120

Q13. Which is the quickest measure of dispersion to compute?

1. 1. Mean deviation
   2. Range
   3. Variance
   4. Coefficient of Range

Ans: B. Range

Q14. The central fifty per cent of the observations in a data set are only based on the_________ Measure of dispersion.

1. 1. Quartile deviation
   2. Mean deviation
   3. Standard deviation
   4. All of these

Ans: A. Quartile deviation

Q15. Find the measure of dispersion that can attain a negative value?

1. 1. Standard deviation
   2. Range
   3. Coefficient of dispersion
   4. Variance

Ans: B. Range

Q16.Which measure of dispersion is appropriate to compare the two different series?

1. 1. Coefficient of variation
   2. Mean deviation
   3. Variance
   4. Standard deviation

Ans: A. Coefficient of Variation

Q17. Find the Standard deviation of the first 50 Natural numbers.

1. 1. 10.43
   2. 16.43
   3. 12.43
   4. 14.43

Ans: D. 14.43

Q18. Find the result of the standard deviation result of the following sample data 8,4,6,2,12, and 10.

1. 1. 5.42
   2. 2.42
   3. 3.42
   4. 4.42

Ans: C. 3.42

Q19. Which set of observations has the minimum variation?

1. 1. 30,40,50,60,70
   2. 56,58,60,62,64
   3. 38,39,40,41,42
   4. 50,60,70,80,90

Ans: C. 38,39,40,41,42

Q20. Which methods are used to calculate Standard deviation?

1. 1. Step deviation method
   2. Direct method
   3. Short cut method
   4. All of these

Ans: D. All of these

Q21.In which series of frequency distribution the Range can not be calculated?

1. 1. Open-ended series
   2. Inclusive series
   3. Exclusive series
   4. Unequal class intervals

Ans: A. Open-ended series

Q22. Which one is the most widely used measure of dispersion?

1. 1. Mean deviation
   2. Standard deviation
   3. Quartile deviation
   4. Variance

Ans: B. Standard deviation

Q23. 45,52 and 65 are the variable quartiles, respectively. Find the quartile deviation of this variable.

1. 1. 16
   2. 14
   3. 10
   4. 20

Ans: C. 10

Q24. Which of these is an example of the application of Range in a real-world scenario? 

1. 1. Quality control
   2. Weather Forecasts
   3. Fluctuation in share market 
   4. All of the above

Ans: D. All of the above

Q25.The Quartile deviation with Q1=25 and Q3= 75 is________

1. 1. 50
   2. 15
   3. 25
   4. 20

Ans: C. 25

Q25.There is a set of 5 numbers with variance = 10. If each number is divided by 2, what is the new variance?

1. 1. 0
   2. 20
   3. 5
   4. 2.5

Ans: D. 2.5

Q26. When all values remain the same then the measures of dispersion will be______________

1. 1. 0
   2. Mode
   3. Median
   4. 1

Ans: A. 0

Q27.Find the exact Mean deviation of the values 12,15,and18 is_______

1. 1. 3
   2. O
   3. 2
   4. 6

Ans: C. 2

Q28. Find the variance of the values 3,6,8,9,11,7,10,12 .

1. 1. 4.25
   2. 7.36
   3. 3.46
   4. None of these

Ans: B. 7.36

Q29. What is the shape of the Symmetrical distribution found?

1. 1. Bell-shaped
   2. J shaped
   3. U shaped 
   4. None of the above

Ans: A. bell shaped

Q30. Find the value of Quartile deviation when the Mean Absolute deviation of a set of observations is 8.5.

1. 1. 11.2
   2. 12.3
   3. 9.06
   4. 7.08

Ans: D. 7.08

Q31.Which measure of dispersion is demonstrated in terms of nits of observation?

1. 1. Relative measure 
   2. Range 
   3. Absolute measure
   4. Variance

Ans: C Absolute measure

Q32. Which deviation is a percentage expression of the Coefficient of variation?

1. 1. Quartile deviation
   2. Standard deviation
   3. Mean deviation
   4. All of these

Ans: B. Standard deviation

Q33. Which one of the followings is not considered a measure of dispersion?

1. 1. Mode
   2. Range
   3. Variance
   4. Mean deviation

Ans: A. Mode

Q34. Which one of the followings is the relative measure of dispersion?

1. 1. Mean deviation
   2. Variance
   3. Range
   4. Coefficient of Standard deviation

Ans: D. Coefficient of Standard deviation

Q35. From which value of the series the deviations are taken to calculate the Standard deviation?

1. 1. Quartile
   2. Mean
   3. Mode
   4. Median

Ans: A. Mean

Q36. If the sum of all the squared deviations is divided by the total number of observations that are used to calculate

1. 1. Sample Variance
   2. Population Variance
   3. Sample deviation
   4. Population deviation

Ans: B. Population Variance

Q37.When the Arithmetic mean is multiplied by the Coefficient of variation, what will be the resultant value?

1. 1. Variance
   2. Coefficient of deviation
   3. Coefficient of Mean
   4. Standard deviation

Ans: D. Standard deviation

Q38.Which measure of dispersion ignores the signs of deviations?

1. 1. Mean deviation
   2. Range
   3. Variance
   4. Quartile deviation

Ans: A. Mean deviation

Q39.What is the frequency when it is less than the first quartile?

1. 1. 3N/4
   2. N/2
   3. N/4
   4. All of these

Ans: C. N/4 

Q40. The second quartile, which is denoted by 2, is also known as __________

1. 1. Mode
   2. Range
   3. Variance
   4. Median

Ans:D. Median

Q41. P50 is denoted as ___________ the value 

1. 1. Median
   2. Range
   3. Mode
   4. None f these

Ans: A. Median

Q42. What is indicated by the scatter within a distribution if it is high on each side? 

1. 1. Low uniformity of data
   2. High uniformity of data
   3. Outliers of data
   4. All of the above

Ans: C. Outliers of data

Q43. State the measure used to the extent of variation and determine the degree in a data set.

1. 1. Measures of dispersion
   2. Mode
   3. Measures of Central tendency
   4. Variance

Ans: C. Measures of Central tendency

Q44. What is the sum of absolute deviations if it is calculated from the Median?

1. 1. Least
   2. Negative
   3. Positive
   4. 0

Ans: A. Least

Q45. What are the means of dispersion which is the most simple?

1. 1. Range
   2. CV
   3. Variation
   4. Standard Deviation

Ans: A. Range

Q46. When the moderately symmetrical distribution mean deviation is 12, find the exact value of the Standard deviation.

1. 1. 24
   2. 12
   3. 15
   4. None of these

Ans: C.15

Q47. The scatteredness in a data set is statistically called________

1. 1. Range
   2. Variance
   3. Discriminant
   4. Dispersion

Ans: D. dispersion

Q48. Which of the following can be the lowest value of variance?

1. 1. 1
   2. 0
   3. 3
   4. -1

Ans: B. 0